Warning: Wikipedia contains spoilers
John Robie, played by Cary Grant, is a "retired" jewel thief called "The Cat" who now spends his time tending to his vineyards in France. There is a series of jewel robberies that resemble his style and the police believe that the cat is up to his old tricks again.
Robie enlists the aid of an insurance man, Hughson (played by John Williams) in order to prove his innocence. Robie's plan is to catch the new cat burglar in the act. To do this he needs a list of the most expensive jewels on the Rivera. The first names on the list are Jesse Stevens and her daughter Francie. Robie becomes acquainted with them in order to stay close to their jewels. Francie (played by Grace Kelly) is suspicious of Robie's motives. She is certain that John Robie is behind the recent thefts, but at the same time she is attracted to him. John Robie plays off any interest in Francie, at least at first.
Jesse Stevens's jewels are stolen and Francie believes that John has taken them. He goes into hiding, believing he knows now who the new thief is, and plans to catch him. He stakes out a house where he believes the new cat will strike. He is attacked and in the ensuing struggle kills a man the police later claim to be the cat. The only problem is that man had a "peg leg" which would have made it impossible for him to climb over the rooftops.
Francie apologizes to Robie for thinking he was the cat and offers to help catch the real cat during a masquerade party. The French police plan to arrest Robie during the party. Robie and Hughson switch places. Robie captures the new cat with the jewels on the roof. After everything is cleared up, Robie returns to his vineyards and Francie races after him to tell him how much she loves him and that her mother will love his home.