Dramatically, Le Samouraï, is not the most enthralling of Melville’s neo-noir films but it is a benchmark of the sub-genre with Alain Delon as the iconically super-cool hitman, Jef Costello.
Jef carries out his job with clockwork precision, with no apparent personal benefit as lives alone in a run-down apartment, his only companion a little bird in a cage and a distant relationship with girl-friend (played by Delon's wife, Nathalie Delon) of sorts, who is also a hooker. After he terminates a nightclub owner he is pursued by a police superintendent (François Périer), double-crossed by his employer but with a new contract to carry out he's not the kind of guy to be frightened off.
All this unfolds with little heat as the phlegmatic Jef goes about his business with what can only be regarded as existential fatalism. a quality which pretty much the alpha and omega of the film.
Although no doubt influential on many film-makers, Jim Jarmusch re-worked it splendidly as Ghost Dog: The Way of the Samurai (1999).
FYI: Apparently the film originally ended with Jef smiling to camera as he fulfils his final contract but Melville changed this when he found that Delon had used the idea in another film.