Jean-Pierre Melville did not invent the noir style. Film-Noir ended in the 50's and the term can be used to described post-Film-Noir films that resemble the style such as Chinatown, Le Samourai, Le Cercle Rouge, Taxi Driver, Memento, Heat, or Collateral. He loved American gangster films and Film-Noirs, and created somewhat of a fantasy world in Le Samourai.

An interesting article stated that the 60's French culture didn't really look like Melville's films fashion-wise and such. It was really a swirl of older films he loved and his own unique style. Personally I don't think Carlito's Way's chase scene is a reference to Le Samourai.

Double Indemnity is a perfect example of an excellent Film-Noir.

SPOILERS FOR LE SAMOURAI
Due to the Samurai theme of the film, I believe the final hit was a setup by his employers. He knew it was gonna end in death, and he accepted that. Costello's decision to take out the bullets was his own Seppuku.
SPOILERS END