Help with travel logistics

Why not keep the rental car the whole time? Turning it in to take a train doesn’t make any sense.

There is a daily direct TGV, at least on the schedule into late December that goes, ..Strasbourg, Colmar, Mulhouse, ....Avignon, Aix-en Provence, Marseille.
Check as you get closer, but it will probably still be on the June-July schedule.

We have driven from Amsterdam to Alsace to Provence then back to Paris. I would keep the car -- and plan one stop between Alsace and Provence somewhere along the Rhone rather than trying to fiddle with dropping and picking up two cars. (there is no five minute grab and go with European car rentals. We have more than once had it take 2 hours to pick up a reserved car. And then you want to get receipts that they aren't damaged and are gassed when you drop and it is not efficient to do so as it is in the US.). We stopped at a little town called Vienne on our trip to Provence; we literally just picked it on a map because we wanted something small and picked it for location. It turned out to be a lovely place to spend an afternoon and morning with lots of interesting Roman ruins.

Hi,
If you would ask me: I would rent a car all the way and plan a few stops along the route. There are some very scenic views

Thanks for the replies- looks like so far most of you would keep the car !maybe the suggestion of stopping somewhere halfway might work .

Kathy, where are you flying from? I.e. which country do you live in?
Basel only has flights to and from Europe, North Africa and the Middle East, plus one weekly seasonal flight to Montréal.
If you are coming from outside Europe and want a direct flight, Zürich would be better.

You cannot (without large extra cost) rent a car in Zürich and return it in Provence. The best option would be train to Strasbourg, 1-2 nights there (where you don't need a car) and then pick up a car, explore Alsace and drive to Provence.

We are from USA.Cincinnati is our closest good airport.On Skyscanner website there appears to be a flight from There to Mulhouse with a stop in Paris.Looks like Delta partners with Air France.

there appears to be a flight from There to Mulhouse with a stop in Paris

That will not be a stop, that will be changing planes. Getting off one plane and getting on another.
I just checked Cincinnati airport (list here: https://en.wikipedia.org/wiki/Cincinnati/Northern_Kentucky_International_Airport#Passenger ), Paris-Charles de Gaulle with Delta appears to be the only direct destination in Europe.

If I were flying into Paris and wanting to get to Alsace, I wouldn't get a plane to Basel. I would get a train direct to Strasbourg, overnight there 1-2 nights and then pick up a car.
There are a number of direct trains from Charles de Gaulle to Strasbourg taking ~1h50. I looked up a random date (next Wednesday) and I can see:

Aeroport Paris-Charles de Gaulle TGV depart 08:59, Strasbourg arrive 10:49
Aeroport Paris-Charles de Gaulle TGV depart 11:24 , Strasbourg arrive 13:13
Aeroport Paris-Charles de Gaulle TGV depart 12:44, Strasbourg arrive 14:45
Aeroport Paris-Charles de Gaulle TGV depart 15:07, Strasbourg arrive 17:01
Aeroport Paris-Charles de Gaulle TGV depart 18:58, Strasbourg arrive 20:58

Plus other options if you change in Paris.

Thank you Cris.We have traveled by train a lot in Europe so that would not be a problem.I imagine picking up a car in Strasbourg would be cheaper than at an airport.Once I get the flights figured out will check with auto Europe for car arrangements.Such great advice from seasoned travelers !

If I were planning it, it would likely be: Fly to Paris (stay at least a couple nights), train to Strasbourg, rent a car to travel through Alsace.

When I went my loop was train to Auxerre, rent a car and drive south through Burgundy to Beaune, then to Colmar and north through Alsace, dropped the car in Strassbourg, train to Reims, train to Paris.

On a different loop it was Paris, train to Lyon, rent a car, drive through Annecy and Chamonix then south through the Ardeche (stopped one night) and on to Arles for five nights around Provence, then to Juan les Pins (drop car) and four nights in the Riviera area, flight from Nice back to Paris.

Based on my experience, if you don't want to see anything between Alsace and Provence, a flight is the best way to cover that distance (probably into Avignon, Montpellier or Marseille). After Provence, same thing.

Contrary to some posters above, I would NOT want to drive between Alsace and Provence. It's a long way, and if you don't have time or interest in Burgundy and Lyon, there's no point really. A train from Strasbourg to Avignon TGV is your best bet between the two regions, or a flight from Strasbourg to Marseille.

I'm with balso. I think your original idea was best. if you reserve in advance, dual short-term rentals are a snap.