In reply to chris_seed:
It does depend a bit on where you intend to climb, and particularly the altitude and the exposure (ie. North or South facing). For example limestone crags at relatively low altitude like the Vercors will be fine in late May ands June, possibly getting a bit hot if in the sun in mid-summer whereas rock routes at altitude, around Chamonix, can still be iced up in June. Around Briancon the same sort of considerations would apply - high rock routes on the Ecrins might be problematic whereas the lower crags would be fine. Whatever you'll always find plenty to do.