The Man on the Eiffel Tower [1949 - USA] mystery

Bill Kirby, a dandy living off his wealthy aunt, states in public that he wishes her dead and catches the ear of Radek, a desperate fellow who is very clever but also a bit loopy. Radek offers to murder the old lady so Kirby can get his inheritance, pay his wife to divorce him, and marry his wife's friend. On the night of the murder, a would-be burglar named Heurtin stumbles upon the corpses of the old lady and her maid. Heurtin, who has poor eyesight, loses his glasses and must be helped home by the killer. Inspector Maigret is assigned to the case and quickly tracks down the owner of the thick glasses found at the scene of the crime. Heurtin helps identify Radek, but there is no real evidence against him. So begins a clever game of cat-and-mouse, in which Radek taunts the police with clues and his dirty money and blackmails Heurtin, then Kirby, and then Kirby's wife and mistress into to helping him, even while Maigret is patiently tailing him, waiting for him to make a mistake.