I’m pretty sure the end of October is too late for the Pyrénées, but I haven’t been in elevation there in October/November.
You will probably need to stay closer to the Mediterranean but at lower elevation, behind the Côte d’Azur or the hills in Occitanie. I spent four months last year in Uzès and think it’s a great base for heading out onto trails. Of couse, a lot of the time we were restricted to 1 or 3 kilometers due to the lockdown, but even with that roadblock, we were able to get into rural areas on foot. There’s a ton more a car ride away. It doesn’t get as much Mistral wind as Provence.
Édit: What Kerouac2 suggested could work since you spoke of huts, etc, which I overlooked in my first answer. The GR guidebooks have lodging listings. You could hike in the Cévennes or Les Causses out of Millau. Another is the stunning Le Puy en Velay on one of the St. Jacques trails. Finally, look at trails through Conques and Rodez, again on the St. Jacques trails. Thèse are all in mountains but lower elevation. These areas are gorgeous.