Complementing and correcting Many of the reviews here included are as good as anyone needs. Therefore, I will not waste your time, nor mine, writing a subjective take on what is a 6 to 8 point movie.
What compels me to write, however, is a correction: the music was not written by Thelonious Monk, as is stated in at least two reviews. The credit goes to pianist Duke Jordan (1922-2006), contemporary and friend of Charlie Parker, except of course, that Jordan lived a much longer life, the last 25+ years (since 1978) in Denmark.
For those who are interested, the full line up in the soundtrack includes: Sonny Cohn trumpet, Charlie Rouse tenor sax, Eddie Kahn bass, and Art Taylor drums. And, if you excuse a bit of trivia: Duke was married with jazz singer Sheila Jordan from 1952 to 1962 (at this writing, Ms Jordan is 89 years old and still performing!).
Concluding, this movie has arguably one of the best jazz soundtracks of the time, not an uncommon event in French film during the 1950s and 1960s (e.g., Miles Davis, Art Blakey). This cool, post-bop, hard bop era was a great creative time for jazz, no doubt. Memorable and rewarded by time till this day.