Bobby Deerfield, a Formula 1 race driver, stands on a track looking at skid marks and searching for clues to a recent crash. Seeing his friend, Bertrand Modave, standing next to his Formula 1 car, Bobby repeatedly asks for a key. He wakes with a start. He turns on the bed lamp, goes to the bathroom, then returns to bed and lies awake in the dark, reliving that day at the track. Fans ask for autographs and chant the name Deerfield. His French girlfriend, Lydia, stands nearby. Bobby gets into his car and takes off with several others. One of the cars hits another and explodes. After Bobby and Lydia attend Modave's funeral, Bobby tells his pit crew that he will not get into another Formula 1 car until they figure out what happened to Modave’s, because their cars are exactly the same. Later, in Paris, France, Bobby connects wiith his brother, Leonard, but the brothers have little to talk about. Bobby does not remember anything from their early home life in Newark, New Jersey, not even the way his Mae West impersonation always made his mother laugh. Bobby’s attitude angers Leonard, who has legal papers that concern their mother’s property, along with a packet of boyhood photographs. Bobby is not interested in the property, and Leonard asks if he wants to be contacted when their mother dies, then knocks Bobby's sunglasses off his face. Later, with Lydia, Bobby speculates that rabbits on the tracks may have caused the crash. He drives to a sanatorium in the alpine village of Leukerbad, Switzerland, where the surviving driver, Karl Holtzmann, recuperates. Staying after dinner, Bobby asks Karl about the crash, but Karl insists that Modave simply misjudged the turn. Bobby disagrees. After Karl is wheeled away, a patient named Lillian Morelli asks Bobby if she can have his butter, and asks disjointed personal questions. The conversation turns to speed, danger and death, but when Bobby says he never thinks about those things, she concludes that racing is boring. After dinner, as they watch a magic show with other patients, Lillian wants to know if Bobby believes in magic, destiny, or God. That night, a nurse comes into Lillian’s room with medications, but Lillian refuses and says that she will come to death on her own terms. Early the next morning, as Bobby prepares to leave, Lillian appears with a bag, wanting to hitch a ride to Florence, Italy. Bobby agrees to let her ride along, but Lillian continues to pick at him about his “feminine touch” on the steering wheel and speculates about his racing car being an extension of his penis. When they go through a tunnel, she tries to get Bobby to scream in the dark with her, because she wants to scream and why shouldn't he? As she screams, Lillian breaks down in tears. They stop for the night at a hotel in Bellagio, Italy. Bobby calls his mechanic in Paris, asking him to pull the steering linkages from his car and Modave’s, and also to have the film of the accident ready when he gets back. At dinner, Lillian calls Bobby a “turtle” because he takes no personal risks despite his dangerous profession. She asks Bobby to hold her, and they return to her room, disrobe and get into bed, where she promptly dozes off. When Bobby strokes Lillian’s hair, some of it comes out in his fingers. Next morning, as they prepare to leave, Lillian wants him to follow a hot air balloon floating in the distance above Lake Como, but Bobby refuses. Later that day, as Bobby drops Lillian off at her uncle’s house in Florence, she runs inside to get a book for him. She tells him she is sorry that he didn’t scream with her or chase the balloon, but she hopes he finds his rabbits. Later, Bobby finds a note in the book that Lillian has written in Italian, which translates as “Everything is sweeter when you take a chance.” Back in Paris, Lydia asks Bobby about his trip and mentions that she ran into a friend who told her he had seen Bobby in Bellagio. At the garage, Bobby reviews footage of the crash. The projectionist slows down the film, then freezes a frame, but Bobby sees nothing that might provide an answer. In preparation for the upcoming 2 May 1976 Jarama, Spain, race, Bobby films a television commercial in Paris. He feels restless, however, and returns to Florence to talk with Lillian’s Uncle Luigi, in hope of finding her. Luigi says that Bobby should forget about Lillian because she is too outspoken and difficult, like her mother, but if Bobby wants to see her, he should come play Bocce because Lillian always comes to watch. She does show up as Bobby and Luigi finish a game, and asks if Bobby is still “driving in circles.” As Bobby and Lillian walk together, she asks him to remove his sunglasses because she hates to see herself in mirrors. He claims to wear them to avoid being recognized, but she bets a wine and cheese picnic that nobody will know him. He takes them off, and as they walk along a block with nobody noticing, Lillian smiles with satisfaction, then shouts “Bobby Deerfield!” A crowd gathers around him. Later, Bobby and Lillian picnic and she criticizes him for never having fun. As she walks away from Bobby, she comes upon the owner of the property, Carlos Del Montanaro, who tells her he’ll be flying his balloon tomorrow. Rejoining Bobby, Lillian tells him a wild story about her father’s death, but then says she made it up. Bobby insists she is keeping emotional distance, but Lillian says that telling a lie is better than making small talk. After they return to her apartment, Bobby and Lillian kiss and then make love. In the morning, Lillian is gone, but she has left a marked newspaper clipping about a balloon regatta in the countryside. Bobby arrives as a half-dozen large balloons are ready to lift off. Lillian is with Carlos and a couple of others. When she asks Bobby to join them, he refuses and the balloon drifts away without him. Bobby and Lydia go to Jarama, but he is distracted and Lydia notices that something is wrong. During the race, as Bobby takes the lead, he fails to make a turn and crashes. He escapes uninjured, but flames destroy his car. Back in Paris, Lydia admits to Bobby that she knows all about Lillian Morelli, and that Lillian is dying. Realizing that Bobby was unaware of Lillian's terminal condition, Lydia regrets telling him. Bobby returns to Florence. He and Lillian argue. She wants him to surprise her and stop being boring, so Bobby imitates Mae West, even though Lillian has no idea who Mae West is. She says, “It’s a beginning.” Bobby shows her the childhood photos his brother gave him. She asks why there are no photos of his mother. During a boat outing, Bobby tells Lillian a story about his mother’s death that intrigues her, but then confesses that he made it up. Lillian laughs and appreciates the lie. As their relationship blossoms, Bobby senses doom hanging over them, especially after Lillian passes out in a shop. One day Lillian tells him she wants to go back to the sanitorium. On the way, a couple of American tourists take their picture and promise to send it to Bobby. However, he gives them his old address in Newark. He stays with Lillian in Leukerbad as she fades away. After her death, Bobby drives back to Paris.