I'm sorry if I asked this question in the wrong category.
Answer Marc,
You're in the right category. This is definitely jazz. It IS however, a small jazz combo consisting only of clarinet, guitar, bass and drums. If you like this style, look up the guitarist Django Rheinhardt. Woody Allen wrote and directed a great movie about his life starring Sean Penn and Samantha Morton called "Sweet and Low Down." VERY interesting. Also, this style is also used by jazz violinist Stephane Grappelli. Look him up too!