There is at least one major climbing shop and at least one substantial modern indoor climbing gym within half-hour drive from Aix-en-Provence (which is not more than an hour's drive from the Calanques). I sort of doubt any of those rents gear that you could take away with you for outdoor climbing. (Note that in USA almost no shops will rent a harness except to someone climbing indoors in their gym, or outdoors under supervision of a professional guide). Possibly could rent shoes? or a crash pad? but better to bring your own rope and draws and harnesses.
They usually don't close the entire Calanques in August for fire hazard. But some of the best climbing sections might be closed. Note that there are several lifetimes of good sport climbing nearby outside the Calanques. Anyway August is likely to be hot, and many of the famous routes in the Calanques face South.
So most serious local climbers who have the freedom to leave and climbing somewhere else, do so in August. . . . (the southeast quadrant France has multiple lifetimes of great climbing at higher altitude with cooler temperatures).