We left Arles on 22 March this year. Finished at Puente about 41 days later. Did not need sleeping bags. Every place had blankets. It was the coldest spring they've had in this part of France for years. And that's not my opinion - that was the general comment from the French locals.
However, September could still be pretty warm. It's your call, but if I was doing Arles to Castres in September I'd not take a sleeping bag.
One thing: the blankets can be rough textured. They might irritate sensitive skin. A silk body bag to slip into solves that.