Turnbull's right to mention French film noir. Big up to Jean-Pierre Melville: Le samourai (1967) and Le cercle rouge (1970) are both pretty amazing. I called the former film my favourite for quite some time; not seen it in a while though. Melville made others, too.
I watched
Le doulos last week, and can report it's definitely worth seeing, though perhaps not before the other Melville films. (From what I've seen, Melville's best film by some stretch isn't a gangster film but a war film, called
Army of Shadows.)