If you like trad jazz, Le Petit Journal Saint-Michel is the place:
http://claude.philips.pagesperso-orange.fr/
You may be lucky to attend a terrific stride piano concert by the great master Louis Mazetier.
BTW, try to get a table near the piano!
Second place for older jazz styles is Caveau de la Huchette:
http://www.caveaudelahuchette.fr/1571/index.html
Nice spot!
I caught a wonderful performance of Claude Tissendier's Big Band a few years ago!