The next morning, as Robie is visiting with Mrs. Stevens in her suite's sitting room, Hughson arrives to provide details of the previous night's burglary (of gems that were insured for $35,000 for another client, Mme. LaRue - "wife of a high government official"). He suspiciously eyes Robie as he mentions the probable burglar, the Cat, and as he pleads once more to Mrs. Stevens to keep her jewelry in the hotel's safe. In one of the most memorable and vulgar images on screen, Mrs. Stevens extinguishes her cigarette (a phallic symbol) in the yolk of a fried egg, [In another earlier Hitchcock film Rebecca (1940), the elderly dowager extinguished her cigarette in a jar of cold cream.] - as she retorts back: "If you haven't any guts, why you shouldn't have taken my bet." She has little love for her valuables:

I have no more affection for that jewelry than I have for a train ticket that gets me somewhere.

When Francie arrives (after sending for Robie), she invites him to join her for a swim. He replies cleverly: "I think I can manage to stay afloat, thank you." Robie avoids confirming an afternoon meeting with Hughson by giving the excuse that he will be investigating furnished villas for rent: "I might even retire here...Quite a few of the roofs need careful examination." Shortly afterwards, Robie meets Frances in the foyer - she attracts attention by being fashionably decked out in a high-necked, black bathing suit, oversized white sunhat, and white coverup. When he drops his room key off at the desk, the concierge passes him a handwritten note on Carlton Hotel stationary:

Robie
You've already used up 8 of your 9 lives.
Don't gamble your last one.

Danielle is on the beach and entices Robie to swim out to the hotel's floating raft. While she reclines on the raft and he holds on to the ladder, she accuses him of committing the jewelry robbery, and then lounging around with an "American beauty" (his "next victim") under the beach umbrellas. She tells him that his old friends from the Resistance in the restaurant still hate him (and vow to kill him), or want him to get caught, to avoid being sent back to prison.

In the film's famous, classic 'cat-fight' scene, Danielle again invites him to join her in South America just as Frances swims out. He pretends he has just met Danielle and then helplessly looks back and forth at the two feline women while they tread water on either side and flirtatiously fight over him.

Danielle: Don't you think it's foolish to remain here without knowing what will happen to you? But if you were in South America with me, you will know exactly what will happen.
John: You make it sound dangerous either way.
Danielle: It would be so much nicer to be killed by love, no?
John: Ah, pardon me while I get the water out of my ear.
Danielle: John, you know what sort of men they are at Bretani's. Another robbery and they will do something to you.
John: Well, I'd better get back.
Danielle: But what has she got more than me - except money, and you are getting plenty of that.
John: Danielle, you are just a girl. She is a woman.
Danielle: Why do you want to buy an old car if you can get a new one cheaper? It will run better and last longer.
John: Well, it looks as if my old car just drove off.
Frances: No, it hasn't, it's just turned amphibious. I thought I'd come out and see what the big attraction was. John: Yes.
Frances: And possibly even rate an introduction.
John: (to Danielle) Oh, uh, you didn't tell me your name.
Danielle: Danielle Foussard.
John: Miss Foussard - Miss Stevens.
Frances: How do you do, Miss Foussard. Mr. Burns has told me so little about you.
John: Well, we only met a couple of minutes ago.
Danielle, That's right, only a few minutes ago.
Frances: Only a few minutes ago. And you talk like old friends. Ah well, that's warm, friendly France for you.
John: (To Frances) I was asking about renting some water-skis. Would you like me to teach you how to water ski?
Frances: Thank you, but I was women's champion at Sarasota, Florida last season.
John: Well, it was just an idea.
Frances: Are you sure you were talking about water-skis? From where I sat, it looked as though you were conjugating some irregular verbs.
John: Say something nice to her, Danielle.
Danielle: She looks a lot older, up close.
John: Ohhh -
Frances: To a mere child, anything over twenty might seem old.
Danielle: A child? Shall we stand in shallower water and discuss that?
Frances: Enjoying yourself, Mr. Burns?
Robie: Oh yes, it's very nice out here, with the sun and all.
Frances: Well, it's too much for me. I'll see you at the hotel.
John: (laughing nervously) I'll go with you.
Danielle: But Mr. Burns, you didn't finish telling me why French women are more seductive than American women?
John: I know what I'd like to tell you!

When he later retrieves his jacket from his dressing room, he notices that Hughson's list of clients is marked with a wet thumbprint. He is followed by a police detective as he walks up to the Carlton Hotel. Frances has already changed and is standing with her hands on her hips at the hotel entrance:

Frances: Do you have time for me, now?
John: I'm sorry I was so long out there at the float.
Frances: From what I saw of that girl, I thought you'd be a lot longer.

Rather than join him for cocktails at six that evening, she has immediate plans to invite him for a basket lunch and a drive in her open sports car [a Sapphire Blue 1955 Sunbeam Alpine Roadster] to see prospective villas for rent. She offers to be his personal tour guide: "We are bound to get lost - a perfect stranger that doesn't know a word of the language?" He concedes to her offer of a "wholesale rate" with "no tipping" after noticing being observed by the detective: "I must say your terms are generous."

In one of the film's many funny-mean love scenes, she opens the conversation during their drive by inquiring about her abrupt kiss:

Francie: I've been waiting all day for you to mention that kiss I gave you last night.
John: You know, back home in Oregon, we'd call you a headstrong girl.
Francie: Where in Oregon, the Rogue River?
John: Where were you born?
Francie: In a taxi halfway between home and the hospital. I've lived in twenty-seven different towns and cities.
John: Was somebody chasing you?
Francie: Boys.
John: Well, you can stop running now.

The juxtaposition of sex with money is first mentioned here, when Francie uneasily confesses the mercenary motivations of most of her suitors. He compliments her - using a financial metaphor of "jackpot":

Francie: I had the funny feeling that all they wanted was to get their hands on my money.
John: Oh, I'm impressed. Well, on second thought, back home in Oregon, we'd have called you a rich, headstrong girl. That would have made it all right.
Francie: Money handles most people.
John: Do you honestly believe that?
Francie: I've proved it.
John: You're a singular girl.
Francie: Is that good or bad?
John: Oh, it's good, it's quite good. You know what you want. You go out after it and nothing stops you from getting it.
Francie: You make it sound corny.
John: Oh no, you're a jackpot of admirable character traits.
Francie: I already knew that.
John: Yes, I will say you do things with dispatch. No wasted preliminaries. Not only did I enjoy that kiss last night, I was awed by the efficiency behind it.
Francie: Well, I'm a great believer of getting down to essentials.

He asks what she expects out of him, and she slyly replies: "Probably a lot more than you're willing to offer." He accuses her of being in Europe to buy a husband, but she counter-challenges him by denying that she mixes husband-hunting with money. When they arrive at the Sanford villa, they walk through the grounds and continue their sparring conversation (as he surveys the roof and gutter pipes for access):

Francie: The man I want doesn't have a price.
John: (chuckling) Well, that eliminates me...
John: You're absolutely right. Give me a woman who knows her own mind.
Francie: No one would give you a woman like that. You have to capture her.
John: Any particular method?
Francie: Yes, but it's no good unless you discover it yourself.

Francie admits that she isn't spoiled by her own level of wealth [Ironically, Grace Kelly, as Francie, became royalty as Princess Grace of Monaco]:

Palaces are for royalty. We're just common people with a bank account.

He notes that she never wears jewelry and she explains why. She is nervous, insecure and defensive about her own husband-hunting, and her fabulous wealth and beauty. She is also jealous of the teenaged brunette Danielle, and how he may have presented an over-inflated image of himself to her. When Francie hints at marriage, he shows little interest:

Francie: I don't like cold things touching my skin.
John: Why don't you invent some hot diamonds?
Francie: I'd rather spend my money on more tangible excitement.
John: Tell me, what do you get a thrill out of most?
Francie: I'm still looking for that one...
John: You are husband-hunting after all.
Francie: That wasn't jealousy you heard working, merely disappointment in your limited imagination. Teenaged French girls yet. Oh, I bet you snowed her under. The big handsome lumberman from America. I'll bet you told her all your trees were Sequoias.
John: You know, that certainly sounds like jealousy to me. Don't be ashamed of it - let it out.
Francie: You're somewhat egotistical.
John: Fighting fire with fire. Miss Stevens.
Francie: Yes, Mr. Burns.
John: You know what I think.
Francie: About what?
John: You.
Francie: I don't really care. Tell me.
John: You're an insecure, pampered woman accustomed to attracting men. But you're not quite sure whether they're attracted to you or to your money. You may never know.
Francie: Anything else?
John: What you need is something I have neither the time nor the inclination to give you.
Francie: Oh, and just what is that?
John: Two weeks with a good man at Niagara Falls.

When their drive continues, it becomes a high-speed chase along treacherous mountain roads to elude the police following them. [Ironically, Grace Kelly was killed in an automobile accident along these very roads in the fall of 1982.] Francie calmly holds onto the wheel with her dainty white gloves as she screeches their motor car around cliff-edged curves. In contrast, he is tense - exhibiting tense fists and sweaty palms resting and rising on both of his thighs. She barely misses running down an elderly woman carrying laundry across a village street. They pass and miss hitting a chicken in the middle of the road, but the detectives have to swerve to avoid the same bird and crash into a stone wall (off-screen). They phone in a report:

We are poulet. [In French, 'poulet' means both chicken and a term of abuse for police.]

When he cautions her to slow down, she declines: "And let them catch us?" And then she reveals, while admitting that she is stimulated, fascinated and thrilled by her knowledge, that she knows that he is not Conrad Burns - but "John Robie, the Cat...one of the world's cleverest jewel thieves." She guessed his criminal record because the police were trailing him - although the glamorous identity that she has fallen in love with is one that he must stubbornly deny and sidestep.

At their secluded picnic spot overlooking the seaside town, they share the contents of her picnic basket in the front seat. (He sits on the floorboard with his legs out the open passenger door.) Their conversation is particularly saucy and filled with witty double entendres and sexy innuendo. In a famous line, Francie makes an offer to Robie, referring to the fried chicken she has brought on the picnic:

Francie: Do you want a leg or a breast?
John: You make the choice.

[The chicken that both cars failed to kill on the road now turns up on their lunch menu.] Although he asserts that she is mistaken about him, she confirms that she has found out his real identity:

Francie: I've never caught a jewel thief before. It's stimulating. It's like...
John: ...like sitting in a hot tub?

Her accusatory evidence is summarized: (1) she read all about him in the Paris newspaper; (2) she first saw him dropped off at the shore of the Cannes beach from a motorboat "driven by that little French girl"; (3) two days later, he showed up at the Carlton Hotel as "Mr. Conrad Burns, just over from America," but he doesn't convincingly act like an American ("a rough lumberman from the big Northwest"); and (4) he only looked at Mrs. Stevens, not at her, because of her mother's jewelry. Francie asks if he plans to rob her mother or somebody else, and then suggests their "next job" together. He denies being involved at all:

Francie: I think Lady Kenton should be our next job.
John: Now listen. (He firmly grabs her wrist.)
Francie: Isn't she on your list? She ought to be. Kenton jewels are famous. I know every inch of her villa.
John: I can already hear your next line.
Francie: The cat has a new kitten. When do we start?
John: Don't talk like that.
Francie: You're leaving fingerprints on my arm.
John: I am not John Robie the Cat.

She also knows that the Sanford villa they visited wasn't for rent. She announces that she will be attending an 18th century costume-ball party at the villa in a week. She comments on his "very strong grip" on her arm - "the kind a burglar needs." He uses the tight grip to his advantage, and pulls her down on top of the picnic basket to 'steal' a kiss from her and make her part of the lunch feast.

She invites him for cocktails at 8 and dinner at 8:30 - "all in my suite." She entices him with both a promise and a threat:

John: I can't come. I'm going to the casino and watch a firework display.
Francie: You'd get a better view from my place.
John: Already got another date.
Francie: Everywhere you'll go, I'll have you paged as John Robie the Cat. 8 o'clock, and be on time.
John: I haven't got a decent watch.
Francie: Steal one.

On the telephone, Robie speaks to Bertani and learns that his restaurant and staff will be providing "food and drinks" for the party in the Sanford villa the following week:

Bertani: There will be many women, rich jewels.
Robie: Just the bait I need.
Bertani: Something the Cat can't resist, huh?