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i'm not a huge noir fan though i do have my favorites (in a lonely place, pickup on south street, out of the past, touch of evil, any noir billy wilder did) but this ranks up there with almost any american noir i've seen.

I agree.
Every single element is brilliant, the tone is just perfect.
The final shot of the photograph fading is quite reminiscent of Memento, another brilliant film, a neo-noir.
It captures a lot of depth, and it does lack the snappy dialogue of a Raymond Chandler adaptation, but makes up for it with the perfect atmosphere.

The French style of neo-noir (this movie, Melville, etc.) was different from the American style, but the thing that I miss the most about the American style is the snappy and cynical script (see Double Indemnity, Out of the Past, In a Lonely Place, etc.)

I saw this again last night. It's one of the best noirs I've ever seen. That gorgeous B & W photography, the memorable jazz score from Miles Davis, the beautiful Jeanne Moreau, and a great plot add up to one terrific film.
"Dry your eyes baby, it's out of character."