Panic (2000) on Netflix

Alex, a sad-eyed mournful man, goes into psychotherapy: he discloses he's a hit man. He also tells the doctor, after a few sessions, that he's attracted to a young woman he's met in the waiting room. She's Sarah, 23, quick, edgy, and perhaps attracted to him as well. But he's married, the dutiful father of a young precocious boy, so Sarah brushes him off. In flashbacks we see him get his start as a killer, at his father's prompting: it's the family business. Dad gives Alex his next assignment: to kill the therapist. Alex keeps returning to Sarah, calling her, stopping by her apartment, as he decides what to do about the hit, his father, his marriage, and his malaise.