ViaMichelin.com suggests three possible routes. I liked La Rochelle on the western route, and I know Chartres and Le Mans are also highly recommended. Poitiers is a good stop on the central route with its very old churches and beautiful, historic upper town. The eastern route includes Limoges, known for decorative-art museums; Oradoue-sur-Glane, site of a Nazi atrocity during WWII; and Perigueux, an attractive e Dordogne town of 30,000.
I didn't much care for Biarritz, but I know it didn't help that I was dealing with a lot of rain during that day trip. I much preferred Bayonne. With a car you'll be able to explore the outline villages I didn't see. How much time will you have? There's lots to see on the Spanish side of the asque Country. Hondarribia, San Sebastian, Bilbao and Vitoria-Gasteiz are all worth visiting, but there are many smaller options as well.
Most folks who go to Bordeaux seem to head next to the Dordogne and/or the Lot.