We will have 12 days to spend in France, 4 of which we have to be in Bordeaux. Suggestions for an itinerary, please. We’re not interested in going back to Paris.
Since I know absolutely nothing about you, I have absolutely no suggestions. I post only to say that the weather can be very pleasant in September.
Planning someone else´s itinerary from an internet forum is simply an impossible task. You have two basic options:
Spend some time with a few travel books or guides and return with question about your research and ask for suggestions on how to put your ideas to work.
Consult with a travel agent who can help you.
If you rent a car you can easily get to St Emilion and then the Dordogne, perhaps staying in charming Sarlat. The area can absorb your remaining days or you could travel on to another location. I agree with the others you need to do your research and define your interests. This being the RS forum, his France guidebook is a good place to start.
Preview the coverage you'll find in Rick's guidebooks with pages such as these, especially the "At a Glance" section:
https://www.ricksteves.com/europe/france/dordogne (in France book)
https://www.ricksteves.com/europe/france/basque-country (in Spain book or Basque Snapshot book).
I highly recommend watching the RS tv shows for ideas. He has a great one on Dordogne, I believe several of the Loire. If you might be interested in Basque France, I believe it is covered with Basque Spain. I love watching the RS tv shows and other videos for travel ideas.