In a Parisian café, American Bill Kirby, his wife Helen and his flashy lover, Edna Warren, discuss Bill's rich, elderly aunt, Juliet Henderson, who refuses to give her ne'er-do-well nephew any of her money prior to her death. Edna then coaxes Bill into revealing their affair to Helen, and the hurt but pragmatic Helen agrees to grant her husband a divorce on condition that she receive a handsome settlement. When Edna immediately insinuates that she will leave Bill unless he obtains some money, Bill jokingly suggests that he would pay one million francs to have his aunt killed. Moments later, Bill finds a note by his feet, in which the writer, "M. V.," obtusely accepts his recent "proposition." To decide how to respond to M. V.'s offer, the capricious Bill rolls a pair of dice, which come up "aces." That night, Joseph Huertin, a timid, nearsighted knife grinder whose beautiful wife Gisella berates him for being poor, breaks into the Henderson home intending to rob the place, but finds Bill's aunt and her maid stabbed to death in a bedroom. When a terrified Huertin trips while fleeing, his glasses fall off, and the women's attacker deliberately crushes the spectacles with his foot. Outside, the almost blind Huertin meets up with his coldblooded accomplice, Johann Radek, a man who had been eavesdropping on Bill's conversation at the café. Before leading him home, the self-assured Radek tells Huertin that, although he will be arrested for the murders, he, Radek, will get him out of jail. The next day, police inspector Maigret arrests Huertin, having found his glasses, and interrogates him at the jail. Sure that the knife grinder could not have made his way home unaided, Maigret tries to pry Radek's name out of Huertin, but fails. Hoping that Huertin will lead him to his accomplice, Maigret then allows him to escape from prison and has plainclothesmen Janvier and Dufour follow him to a cheap hotel. The next morning, however, an anonymous letter appears in the newspaper, claiming that the police freed Huertin out of desperation. When Janvier, anxious that Huertin not see the letter, inadvertently frightens him and then loses him, Maigret's methods are called into question by his superior, Comelieu. The unflappable Maigret, however, sends the original letter to a handwriting expert, who notices that it has coffee stains on it. Maigret then goes to the same café where Bill received his note, which is in the area where Huertin peddles his skills, and waits. Eventually, Maigret sees Huertin peering inside, furtively looking at Radek, who is eating yogurt and sipping coffee. The clever Radek deduces that Maigret is a policeman and, to scare off Huertin, gets himself arrested. At the police station, Maigret questions the Czech-born Radek, who reveals that, as a youth, he studied medicine while being supported by his now-deceased mother Elizabeth. Maigret then interviews one of Radek's professors and learns that Radek is a manic-depressive, brilliant but unbalanced. Radek, meanwhile, eludes the plainclothesmen who trail him after he is released and makes his way to his mother's house. After his very much alive mother agrees to shelter Huertin, Radek orders the fugitive to remain in her cellar. Maigret, meanwhile, secures the serial numbers from money that Bill receives at his hotel and later finds Radek at the café. The ever-cocky Radek is confident that the detective will be unable to link him with the murders and invites him to lunch at the Eiffel Tower. There an excited Radek teases Maigret by paying for the meal with Bill's money and calling the police investigation inept. Later, Radek contacts Bill and tells him that the police are reopening the case and will be searching for the murder weapon, a fingerprint-smudged knife that Radek claims he left somewhere in his aunt's house. Insisting that Bill will be implicated in the crime if the knife is found, Radek convinces the American to hunt for the weapon himself. When Maigret shows up later at the Henderson house, he finds Bill shot, an apparent suicide victim. Shortly after, the police track down Radek's mother and arrive at her house in time to save the suicidal Huertin from hanging. Unaware of Huertin's capture, Radek continues to goad Maigret, and while being followed openly by the detective, writes threatening letters to Edna and Helen, ordering both of them to go to the Henderson house to look for the knife. Radek's cat-and-mouse game finally ends at the Henderson house when Maigret has Huertin confront the psychopath and identify him as his double-crossing accomplice. Maigret also coyly reveals that the letters were intercepted and that both Edna and Helen, who Radek hoped would murder each other, are cooperating with the police. As he is being arrested, however, Radek escapes the house and runs to the Eiffel Tower, where he is pursued to the top by both a revenge-mad Huertin and the police. Unable to throw himself from the Tower, Radek gives himself up. Then, while the vindicated Huertin happily reunites with the remorseful Gisella, Radek faces execution at the guillotine.
