A veritable institution, La Bellevilloise in Ménilmontant is the multicultural venue to try. It hosts a lot of free concerts, including radio station Radio Nova’s well-known Nuits zébrées. Free invitations to attend one of these concerts can be picked up from the radio station’s offices at 127, Avenue Ledru-Rollin, Paris 11th.
Many of the other concert-hosting cafés are located in Bastille, like Le Motel, the Zéro Zéro, La Mécanique Ondulatoire and Les Disquaires. Good addresses elsewhere in Paris include Le 9b (Belleville), Truskel (Bourse), Le Pop-Up du Label (Daumesnil) and L'International (Oberkampf).
Alternatively, you can attend a free mini-concert at the Fnac, which regularly organizes ‘showcase’ gigs at some of its stores.
Some of the concerts at major festivals are also free: these include the Chorus des Hauts-de-Seine festival, 36h de Saint-Eustache, LaPlage de Glazart, Jazz à Saint-Germain-des-Prés Paris and Villette Sonique. And of course the Fête de la musique on 21 June is the ultimate music celebration.
The website lylo.fr has a comprehensive list of free music events: see the ‘Concerts gratuits’ section.