Any French person with three months to spend on vacation from September to November would start in the Dordogne and end in Provence. For many logical reasons: the weather, the crowds, the vibe, the prices.
But if you've already booked your accommodations... it's too late; at least you can hope that, due to climate change, the weather won't be too bad in the Dordogne in November. Last year, there were a few sunny days in November when we ate lunch outside, but also a few cold mornings with frost.
Three weeks in Beynac-et-Cazenac in November is probably a bit too much.
Outside the tourist season, many shops are closed, you'll basically find a bakery and a mini-market, not much else. The morning markets are open as they do in summer, but obviously, there are no more summer products (although there's still foie gras!).
There are less than 500 inhabitants in Beynac-et-Cazenac (many of them retirees). In all these villages in this very rural region, the non-retirees work during the day and go back home for dinner and watch TV.
In November, there are no more activities for passing tourists, and no more activities like kayaking.
But maybe that's what you're looking for...
Alternatively, you could stay in a big city and explore the surrounding area from there. For example, from Brive-la-Gaillarde or Perigueux.
There are also plenty of other options between Provence and the Dordogne.
Toulouse, the Pink City (and France's fourth-largest city), can be an excellent base for exploring the region.
From Toulouse, you're no more than a 2.5-hour drive from many places. The Dordogne, the Pyrenees, the Tarn Gorges, the Atlantic coast with Bordeaux, the Mediterranean coast with Collioure, Montpellier, Perpignan, etc.
Carcassonne, Albi, the Canal du Midi can be reached in 1 hour...
It's up to you.
https://www.toulouse-tourisme.com/en/