The first composition that is what I would deem the film noir genre of music is Mozart's Requiem III. Sequentia- Lacrimosa. This is part of Mozart's last composition. He was very ill at the time of writing it and actually passed away before it was complete. The piece is heavy in nature; the words that are part of the mass are depressing. The composition is centered around death and the judgment of man. Film noir is not part of a peaceful and simply wonderful world, just as the requiem. Requiem literally means "A Mass for repose of the souls of the dead," there are no happy movements. The genre of film noir does not show happiness, it is about the true nature of people and what life really is, dirty. Maybe this example is a bit more than what film noir is about, but I believe you get the same overall feeling.
The piece, which developed my thoughts of film noir and music, was actually Adagio for Strings by Samuel Barber. The piece is touching on a whole new level. It is beautiful without the normal distinct marks of beauty within music. Film noir lets us all see the truth of human life, the part that is for the most part hidden until some action brings it out. Adagio for Strings was first performed in 1938, at the end of the Depression and the beginning of Hitler's Germany. Life was not so happy for many people and the Adagio seems to portray this perfectly. There is no grand part in the music, it just seems to grow and continue on until it diminishes in the end. There are no happy endings in film noir and there is no happy end to this composition. Film noir easily can be a genre found within music, somber and somewhat disheartening.