While on a skiing holiday, simultaneous interpreter Regina “Reggie” Lampert tells her friend Sylvie that she has decided to divorce her husband Charles. She also meets a charming American stranger, Peter Joshua. On her return to Paris, she finds her apartment stripped bare. A police inspector notifies her that Charles sold off their belongings, then was murdered while trying to leave Paris. The money is missing. Reggie is given her husband’s travel bag, containing a letter addressed to her, a ticket to Venezuela, passports in multiple names and nationalities, and other items. At Charles’s sparsely attended wake, three men show up to view the body. Each of them tests the body to ensure that he is dead.
Reggie is summoned to meet CIA administrator Hamilton Bartholomew at the U.S. Embassy. She learns that the three men at the wake are Tex Panthollow, Herman Scobie and Leopold W. Gideon. In World War II, they, Charles, and Carson Dyle went on an OSS operation to deliver $250,000 in gold to the French Resistance, but instead, they stole it for themselves. Dyle was fatally wounded in a German ambush, and Charles double-crossed the others and took all the gold. The three survivors are after the missing money, as is the U.S. government. Bartholomew insists that Reggie has it, even if she does not know where it is. He tells her she is likely in great danger.
Peter locates Reggie and helps her move into a hotel. The three criminals separately threaten her, each convinced that she knows where the money is. Scobie then shocks Reggie by claiming that Peter is in league with the trio, after which Peter confesses to her that he is really Carson Dyle’s brother, Alexander, intent on bringing the other men to justice because he believes they murdered Carson.
As the hunt for the money continues, first Scobie is found murdered, then Gideon. Then Bartholomew informs Reggie that Carson Dyle had no brother. When she confronts him, Alexander admits he is actually Adam Canfield, a 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. When they spot Tex there, Adam follows him. At the sight of stamp-selling booths, Adam and Tex each realize that Charles must have bought several extremely rare and valuable stamps which he affixed to an envelope that has been in plain sight among his possessions. Both men race back to Reggie’s hotel room, only to find that Reggie has given the stamps to Sylvie’s son Jean-Louis for his collection. At the market, Reggie also realizes the envelope’s significance. She learns that Jean-Louis sold the stamps to a trader, who gave the boy 10 francs’ worth of stamps in return. The trader admits that the valuable stamps are worth $250,000 in total and returns them to her.
Back at the hotel, Reggie finds Tex’s body with the name “Dyle” scrawled next to it. Convinced that Adam is the murderer after all, a frightened Reggie telephones Bartholomew, who tells her to meet him at the Colonnade at the Palais-Royal. As she leaves the hotel, Adam spots her and gives chase. At the Colonnade, Reggie is caught out in the open between the two men. Adam tells her that Bartholomew is really Carson Dyle; he survived the German ambush and became obsessed with exacting revenge on his ex-comrades and reclaiming the treasure. After another chase that ends in an empty theatre, Reggie hides in the prompt box. Dyle discovers her and is about to shoot when Adam activates a trapdoor beneath his feet, causing Dyle to fall to his death.
The next day, Reggie and Adam go to the embassy to turn over the stamps, but Adam refuses to go in. Inside, Reggie discovers that Adam is really Brian Cruikshank, the government official responsible for recovering stolen property. His true identity revealed, he proposes marriage.
The film 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.