Crazy in the Noodle(1957)

Pierre Cousin, a depressive compositor, wants to die. After five vain attempts at committing suicide, he decides to hire professional hit men to do the job on him. But as he's waiting for death, he accidentally saves a suicidal young woman's life... and falls in love. Having suddenly found a reason to live, he now fears the killers he himself hired. Is there still time to call off his contract?