I would disagree that you don't need air conditioning. You might not need air conditioning, but early September in Paris last year was absolutely miserable, with temperatures at 97 and 98 degrees F (and the city is a heat pump as the buildings were built to retain heat during long wet cool winters, and it's one of most "mineral" cities in the world).
You could also get lucky and be here when days are in the 70s, there is no way to know. We don't have a/c in our apartment and it is tough to sleep those hot nights -- but then I go to my air-conditioned office during the day, I am not out trying to tour around. As someone from Oklahoma, I can attest that 97 degrees in Paris is a lot more unpleasant than 97 degrees at home.
People's tolerance for heat varies, of course, and maybe the OP will do fine without air conditioning. But to dismiss it out of hand seems to me to betray a lack of knowledge of Paris in September these past few years.
Sam, be aware that September is the most expensive month of the year in Paris for hôtels, so be prepared for sticker shock !