Doesn't have to be jazz. I think trip-hop and other styles could work great too. Maybe some post-punk entries could hangover into this.
There are some trip-hop songs that could work, yes. Portishead music particularly often has a very noirish feel about it. And yes, over the last few decades there have been a few neo-noir films which have had a modern punk edge to them, so yes, certain moody post-punk entrees could work as well. Modern neo-noir films have untilised a wide range of musical genres over the years. That said, when I think of film noir I tend to think about films from the 1940s and 1950s. And the vast majority of these films are enhanced by moody jazzy soundtracks.
I must confess, classic 1940s Film Noir movies are a great passion of mine. I adore the black and white films from that era and along with 1930s/1940s screwball comedies, and 1960s European new wave films, those 1940s film noir pictures are ones that I still most enjoy watching. Yeah, given the choice between a 1940s film directed by Robert Siodmak, Otto Preminger, Nicholas Ray or Fritz Lang and a contemporary movie I will always opt for the 1940s flick.
Robert Mitchum, Peter Lorre, Gloria Grahame, Humphrey Bogart, Veronica Lake, Barbara Stanwyck, Gene Tierney, John Garfield, Edward G Robinson, I love all these guys and gals so much.