A part from Charlie's pub on the village square that occasionally offers live music, you have to watch for the events calendar (see at the Mairie) of what is going on in the Salle Jean Monnet, Salle de l'Allondon and the new theatre which will be inaugurated soon. If you're willing to leave St Genis, there's a small bar in Peron that organizes concerts. It's called Blue Moon Café
http://www.bluemooncafe.fr
Otherwise, there will be some concerts on 21 June for the Fête de la Musique and of course there are the various concerts organized by the CERN rock and jazz clubs.
It's not exactly a wild musical scene, but still, there are some things happening if you look out for them.
Cheers!