At the Wilton Nuclear Plant, two intruders come over the wall and break into an office. They find plans and take photos of them, but a guard notices the broken window and enters. The leader shoots and kills him and the two men quickly leave by another window as the guard’s partner arrives in time to hear the first guard tell him that two men were there taking photographs.
The next day, the police arrive at the airport and have the passengers for Flight 447 present their luggage for inspection. Peter and Diane are among the passengers, and are surprised that their luggage is being inspected on the way out of the country. The thief, Walker, is present, next to puppeteer Penny Page. When she sets her mink coat down on the counter, Walker cuts open the coat and slips a canister of microfilm into the lining. Diane notices him doing so, while Penny explains that she’s going on a trip to present her puppet show in Paris. Meanwhile, another official approaches Walker and calls him aside for a search.
Peter and Diane are checked through and the custom official explains that it’s routine. Meanwhile, the airport officials find nothing in Walker’s clothing or belongings. Satisfied, they wish him a pleasant journey and let him go. The plane leaves and Diane tells Peter what she saw, but he doesn’t find it suspicious and reminds her that they’re on holiday. Walker sits down next to Penny and tries to strike up a conversation with her, but she rebuffs him and he soon leaves. Peter and Diane overhear the conversation but Peter assumes that Walker was just trying to flirt with Penny.
Once Penny goes in the back, Walker sits back down in her seat and starts to go through her coat mink coat. Penny comes back and asks what he’s doing, and he apologizes, claiming it’s a mistake. Peter still doesn’t think anything of it but Diane insists that Walker is a smuggler.
When the plane touches down in Paris, Walker meets with his contact Bunny and tells him that the microfilm is in Penny’s coat. They spot Penny as they come out and Walker tells Bunny to grab the coat and run, get the microfilm, and drop the coat. Bunny does so but a man grabs him as he tries to escape. Walker grabs the man and assures the newcomer that he’ll take care of him, and then “accidentally” lets him escape while holding onto the coat. Penny comes over to recover her coat before Walker can search it and thanks him for his help. The newcomer comes back and Penny introduces him as her husband, Marcel le Magnifique. They recover the coat and leave, while Peter sees the entire thing and admits that Diane was right.
Later, Peter and Diane check into their hotel rooms and Peter calls Sir George at Whitehall to inquire about Walker. He’s seen a newspaper article about the theft of the plans and Sir George confirms that the thieves probably have the plans on microfilm. He suggests that Peter look into it and Peter decides to track Penny down.
Penny is rehearsing her routine at the Blue Jeans Club and Walker goes backstage to check her dressing room. Marcel, a juggler, spots him and asks why he’s hanging around. Walker claims that he has a proposition to make but Marcel refuses to hear it and tells him to go. Once Walker leaves, Marcel goes into the dressing room and contemplates the mink coat. Meanwhile, Walker talks to a waiter about Marcel’s and Penny’s acts, and promises to come back later to see the show.
At the hotel, Peter makes a few calls and Diane finds an advertisement for Penny’s act at the club. They go there and Peter invisibly goes inside while Diane waits outside. He slips into Marcel and Penny’s dressing room while Marcel is preparing for his act, and starts examining the coat. Outside, Walker and Bunny figure it’s time for Marcel to start his performance and Walker goes inside. Penny finishes her act and goes to the dressing room to tell Marcel that he’s on. She starts to undress and Peter quickly leaves. He sits down with Diane and tells her that the coat’s lining had been cut but there was nothing inside.
Walker enters the dressing room and draws a gun on Penny. He orders her to turn over the mink coat and then searches it and discovers that the microfilm is gone. Penny has no idea what he’s talking about and he escorts her out at gunpoint. Outside, Peter assures Diane that the coat was empty and she assures him that there was something there. As Walker brings Penny out, she screams and Marcel hears her. He drives off in pursuit and Peter goes after them in their rental car.
Walker and Bunny drive to their apartment and take the elevator up, shoving past an old woman. Marcel follows them and burst in, shoving past the woman as well. Upstairs, Walker demands to know where the microfilm is but Penny still professes ignorance. He assures her that he’s shot one man to get the plans and won’t hesitate to kill her as well. Walker threatens to cut her face if she doesn’t talk, but they’re interrupted when Marcel storms in. Bunny knocks him out and Penny suggests that Marcel can help them. When he recovers consciousness, Penny confirms that he had the film developed to find out what she was doing in England, and tells Walker that the photos are at Imperial Studios. Walker leaves Bunny to watch them while he goes to the studio.
At the studio, Walker bangs on the door until the photographer answers the door. Walker claims that he’s with Marcel and is there to pick up the photos. When the photographer turns them over, Peter comes in and takes the film. Walker tries to grab it back, tearing up the office, while the photographer calls the police. Peter knocks Walker down, burns the film, and then punches the spy unconscious. When the police arrive, Peter pushes past them and escapes while they arrest Walker.
Peter goes back to the apartment and picks up one of Marcels’ juggling clubs. He advances on an astonished Bunny and knocks him out.
Later, Penny is performing a new act with a Peter Brady puppet. Peter and Diane are in the audience and applaud with the others.