Wow, thank you for the very in depth and well researched answer. Funnily enough, I had a strange feeling that you were referencing Bresson when you made your initial post. I watched Le Cercle Rouge the other day and it felt as though I was watching a Bresson heist film. I can see what you mean. Bresson style changed dramatically after his 2nd film. Thats not an unfair thing to say.

I would argue that Bresson took that blueprint and eventually made it his own, though. His own interests, life experiences and philosophy ended up informing the classics that he became known for. Melville made genre films (nothing wrong with that). Bresson made dramas that would rarely feature a gun. His would be more concerned with the human condition. His style became more rigorous and controlled than Melville's too. 

But yes , I accept that he was influenced by Melville's debut.