Nicole (Audrey Hepburn) lives in Paris, with her father Charles Bonnet. Charles is famous as a wealthy art collector. Charles is really a forger, who has become wealthy selling his forgeries, as items from his "vast collection". Nicole lives in fear that his forgeries will be discovered.
Nicole catches a burglar, Simon (Peter O'Toole) in their home. She shoots him, but it is a mild injury, and she ends up driving him back to his hotel. Charles lends his priceless Cellini Venus statue to a museum. When the museum informs them that it will be appraised for their insurance, Nicole and Charles realize the forgery will be discovered. Nicole enlists Simon to help her steal the Cellini before it gets appraised. Meanwhile, wealthy art collector Davis (Eli Wallach) proposes marriage to Nicole as a ploy to get the Cellini.
Simon and Nicole successfully steal the Cellini. Simon gives the Cellini to Davis, under the condition that Davis never have any contact with Nicole again. Simon is not really a burglar. Simon is actually an art detective and museum security expert. Charles was suspected of being a forger, and Simon was investigating him. When Nicole found him in the house, Simon was there collecting paint chips from Charles's collection. Simon agrees not to expose Charles's past misdeeds, if Charles promises to go clean from now on. Simon and Nicole marry.
The movie ends with Charles welcoming another art collector into his home, implying he will not keep his promise to Simon.
Thanks Joseph C!