Carmen, in a voice over paired with shots of the city and the sea, introduces herself as "the girl who should not be called Carmen." Somewhere a string quartet is rehearsing the late string quartets of Beethoven. The eccentric Jeannot (played by Godard himself) is living in a sanitarium where the doctor threatens to throw him out if he doesn't start to show signs of real illness. Carmen comes to visit him, and it is revealed he is a washed up filmmaker and her lecherous uncle. After getting her Uncle Jeannot to loan her his seaside apartment, Carmen and some others attempt to rob a bank. During the mayhem of the robbery, Carmen comes face to face with Joseph, a comically inept bank guard, and the two immediately fall in love. The string quartet continues to rehearse, inflecting the scenes of the robbery, and vice versa. The narrative link is that one of the members of the quartet is Claire, who is established earlier in the film as a potential love interest for Joseph.
Carmen and Joseph retreat to Uncle Jeannot's apartment, where Carmen recalls childhood incestuous encounters. Carmen tells Joseph, quoting from Carmen Jones, "if I love you, that's the end of you." Joseph is arrested and put on trial, while Carmen escapes with Fred, the leader of her gang. In flashback, Carmen reveals to Joseph that the robbery was intended to fund a larger project, the kidnapping of "a big manufacturer," or his daughter, with a fake film directed by Uncle Jeannot meant to provide cover, a scheme that John Dillinger supposedly once perpetrated. Joseph is acquitted with the help of an impassioned public defender and Claire's moral support. Meanwhile, Fred persuades Uncle Jeannot to direct the gang's film. After receiving a rose from her during the trial, Joseph reunites with Carmen at a hotel where the gang is staying. He plans to renew their relationship and to participate in the kidnapping, but Carmen seems increasingly uninterested in him and the gang ostracizes Joseph. Things go from bad to worse for Joseph as Carmen toys with a young hotel attendant, Fred directs Carmen to tell Joseph it's over, and Joseph forces Carmen into an abject sexual encounter in the shower where he masturbates on her.
The day of the kidnapping arrives, and is to take place in the restaurant in the hotel where the gang has been staying. Uncle Jeannot is present to direct the film (apparently shot on video), along with the string quartet (performing in public at last) and eventually the police (who have followed Joseph). As with the bank robbery, mayhem ensues. Joseph is determined to face off with Carmen alone; a gun goes off between them, and Carmen falls to the floor. Leaving her for dead, the police drag Joseph away. In a stupor, Carmen asks the young hotel attendant what it's called when the innocents are on one side and the guilty on the other, when everything's been lost but you're still breathing and the sun is still rising. "Daybreak," he responds.