Regina “Reggie” Lampert (Audrey Hepburn), on a skiing holiday in Megève, tells her friend Sylvie Gaudel (Dominique Minot) that she has decided to divorce her husband Charles. She then meets a charming stranger, Peter Joshua (Cary Grant). When she returns to Paris, her apartment is completely empty, and police inspector Edouard Grandpierre (Jacques Marin) notifies her that Charles has been murdered while leaving Paris. Reggie is given her husband’s travel bag, containing a letter addressed to her, a ticket to Venezuela, passports in multiple names, and other items. At the funeral, three odd characters show up to view the body. One sticks the corpse with a pin and another places a mirror in front of the body’s mouth and nose, both to verify that Charles is really dead.
Reggie is summoned to meet CIA administrator Hamilton Bartholomew (Walter Matthau) at the U.S. Embassy. She learns that the three men are Tex Panthollow (James Coburn), Herman Scobie (George Kennedy), and Leopold W. Gideon (Ned Glass), the three survivors of a World War II OSS operation. Together with Charles and a fifth man, Carson Dyle, they were to deliver $250,000 in gold to the French Resistance, but they stole it instead. Dyle was fatally wounded in a German ambush, and Charles doublecrossed the others and took all the gold. The three men want the missing money, and the U.S. government wants it back. Bartholomew insists that Reggie has it, even if she does not know where it is.
Peter tracks Reggie down and helps her move into a hotel. The three criminals separately threaten Reggie, each convinced that she knows where the money is. Scobie then shocks Reggie by claiming that Peter is in league with the trio (though none of them trust each other), after which Peter confesses to her that he is really Carson Dyle’s brother, Alexander “Alex” Dyle, and is convinced that the others murdered Carson.
As the hunt for the money continues, first Scobie is found murdered, then Gideon is killed in an elevator. Meanwhile, Reggie falls in love with Alex, but gets yet another shock when she learns from Bartholomew that Carson Dyle had no brother. Confronted with this, Alex now admits he is actually Adam Canfield, an unabashed professional thief. Although frustrated by his dishonesty, Reggie still finds herself trusting him.
Reggie and Adam go to the location of Charles’s last appointment and find an outdoor market. They also spot Tex there, and Adam follows him. It is Tex who finally figures out where the money is hidden. He sees booths selling stamps to collectors and realizes Charles must have purchased rare stamps and stuck them on an envelope in plain sight, the letter in his travel bag.
Adam realizes the same thing and races Tex back to Reggie’s hotel room, but the stamps are gone because Reggie had given them to Sylvie’s boy, Jean-Louis (Thomas Chelimsky), for his collection, and he has taken them to the market to trade them. Reggie now also realizes the stamps’ significance, so she, Sylvie, and Jean-Louis find the stamp trader, Mr. Felix (Paul Bonifas). Fortunately, he is honest. Recognizing the value of the stamps, he guessed that there had been some mistake, so he returns them to Reggie.
Back at the hotel, Reggie finds Tex murdered as well. While dying, he wrote the name “Dyle.” Assuming that Alexander Dyle is the murderer after all, a frightened Reggie telephones Bartholomew, who arranges to meet her. When she leaves the hotel, Adam spots her and gives chase through the streets of Paris and the subway.
At the rendezvous, Reggie is caught out in the open between the two men. Adam tells her that Bartholomew is the murderer — he is really Carson Dyle, who was only wounded by the Germans. (To trick Reggie, he had slipped into an embassy office that was left unlocked at lunch.) After another chase, Adam kills Dyle to save Reggie.
Reggie and Adam go to the embassy to turn over the stamps, but in the corridor, Adam refuses to accompany her further. Going in, Reggie is shocked to find Adam already inside (having slipped in through a separate door). In fact, Adam is Brian Cruikshank, the government official responsible for recovering stolen property. After proving his true identity, he promises to marry her, once she gives him the stamps.
The movie ends with a split-screen grid showing flashback shots of Brian’s four identities, while Reggie says she hopes that they have lots of boys, so they can name them all after him.