My husband and I spent a month in France from mid-September to mid-October. We were in Provence in early October and made all accommodations while we were there. We mostly Airbnb'd and found nice places. We did run into problems finding somewhere to stay while in Aix-en-Provence and needed the tourist office to help us find a place, which ended up being fine but not really what we would have preferred. In my experience I'd say you might be taking a bit of a chance of not finding exactly what you want if you don't book any accommodations for September.
After Provence we booked an Airbnb for several days in Villefranche, which we highly recommend. Beautiful old town, great beach, and although we had a car we took a bus directly to Nice. Try to be in Nice on a Monday for the incredible antique market!