The Owl (1991)

Alex L'Hiboux, a ruthless mercenary-cum-vigilante, is known as 'the Owl' because he never sleeps. His insomnia comes from a combination of a medical disorder and recurring nightmares of the murder of his wife and daughter. Alex is approached by Lisa, a young girl whose father is missing. She awakens painful memories of his own child, but after some persuasion from a policewoman friend, he agrees to help her.