Essentially, film noir refers to a period of film making in the United States developing in the 1940s through the 1950s in which the themes, motifs, and general lighting and appearances were considered dark. It comes from the French word, noir, meaning black or very dark. And these films were indeed very dark and very black in terms of what they were showing movie audiences.
By definition, I would personally define the keyword to identifying such film noir movies as the word, disenchantment. That word, disenchantment, sums it up accurately and without sentiment! Whether it be a villian or a villainess, or a hero or a heroine, there is always the visual and verbal sense of disenchantment present which the viewing audience could readily identify within the film characters. This sense of disenchantment was evident in the way the characters talked, moved, or reacted.
Jazz and related musical scores for these movies generally tried to reflect the feeling of disenchantment. The 1950s in the United States was a time of uneasy answers to uneasy questions that would pave the way for what happened in the turbulent 1960s. The 1950s saw a time of unrest and growing demand for rights for minorities and women. The era of the 1950s was never dull. The 1950s was a decade of silent, repressed rage. If you need a convincing look, take a viewing of the classic 1955 film noir, "The Big Combo," which contained all the elements of great visual style and acting as well as introducing two sexual themes not seen before in film noir, and cast actors perfectly molded for their roles such as Richard Conte, Jean Wallace, Cornel Wilde, Earl Holliman, Lee Van Cleef, Brian Donlevy. The 1950s were anything but dull, and that also applies to jazz music, too!
Looking into the 1950s for jazz, one comes across such musicians as Dizzy Gillespie, Ronnie Scott, Tubby Hayes, Chico Hamilton, Jim Hall, John Lewis, Cecil Taylor, Thelonious Monk, Billie Holiday, Pee Wee Russell, Miles Davis, John Coltrane, Kenny Dorham, Charlie Parker, Art Pepper, Milt Jackson, Bill Evans, Chet Baker, Horace Silver, Ruby Braff, to mention but a few from so many! Each was developing and pioneering musical sounds that are today referred to as classic jazz.
Influences from the film noir sparked influences on the composers and musicians of its era, and those years show the remarkable sounds that developed in various motifs. A lot can be learned from viewing these movies and listening to these jazz creators during the decade of the 1950s, something for jazz listeners to connect with and grasp a clearer vision of what some aspects of 1950s America was all about, and why.
Jazz music remains the subtle lifeblood and unsung hero/heroine of the soul of American music, and the 1950s is a good starting place to explore from. The 1950s in the United States paved the way for many things, many unexpected things!