Drive between Provence and Biarrtz

Two things you can do are to check on viamichelin.com for time (add 25% or so) and tolls, and look on AutoEurope.com for drop off fees. We have never had to pay any; but if they exist, they will be modest compared to cross-border fees.
Cahors, Cordes sur Ciel, or Albi would all be nice places to spend a night; all more interesting than Carcassonne, imo.

If you zoom in on the ViaMichelin route map, the most scenic roads will be bordered in green.

I haven't been to Cordes--I think it's difficult without a car--but liked both Albi and Cahors a lot. Depending on which route option you choose, you could be driving very near the Dordogne River. That's a beautiful area very popular as a vacation destination. If you decide to do this by car and don't anticipate another car trip in that area, I'd try to take advantage of having my own vehicle by hitting one or two of the small villages that are borderline-impossible without a car. I had to miss a lot of lovely-sounding places because I was dependent on trains and buses.

The most direct route is via autovias (interstates) so the view would be like driving on any interstate. The last time I used French interstates there were plenty of tolls. From Vaison-la-Romaine to Biarritz it’s 335 miles. The maximum speed limit would be 130kph (78mph) but can vary depending on weather and the type roads you decide to take. The more scenic views would be via secondary roads but would take longer, and with limited time you’d be best to stick with the highways.

Thank you all for your replies so far. Unfortunately we do not have a lot of time, and this is just a part of a larger itinerary. We will have two nights in Villafranche sur Mer after we fly into Nice, then 2 or possibly 3 nights in the Vaisson la Romaine Area with day trips out. Next is San Sebastian for about a week with day or an overnight or two out from there. The question is do we travel in our car from Vaisson la Romaine all the way to Biarritz in one long day and then take a bus to San Sebastian, or stop along the way and stay in some place like Carcassone. I am curious how scenic it is. I just did a check on different options, flying out of Marseilles, to Biarritz or Pamplona and it seem like it is more expensive and takes more time than driving. Thank you to those of you who recommend the Rome2rio and the Michellin sites. It helps us to figure this all out.

You can also drive to Nimes, return the car there and take the train. From Nîmes it is 2 hours by train to Carcassonne and there are tickets for as little as €10.

Carcassonne is definitely worth a visit, and overnight is the best way to visit. I would do it.

I would also ditto the recommendation to get of the autoroute as much as possible. French autoroutes are AMAZING, easy to drive, fast, lots of service plazas (aires). But there is no view. Maybe take the A9 as far as Beziers to make up some time, then head off onto the D5 and follow the D routes to Carcassonne. If you have even more time, go a bit further north through the Parc Naturel du Haut-Languedoc for even better scenery. You will still get there within 4-5 hours.

Check flights into Bilbao. That's a much busier airport than San Sebastian, I think, and there are frequent buses from downtown Bilbao to San Sebastian (faster than the train). I'm sure there's easy transportation into town from the Bilbao airport, but I've never used that airport.

I am one who likes Bilbao more than San Sebastian; there's more to see there, and it's less touristy.