6 days in France without a car

Avignon - the transportation hub for western Provence. You can easily visit: Arles, Aix-en-Provence, St Rémy, Ile sur la Sorgue, Nîmes, even Pont du Gard and Uzès, among many others.

Bookmarking! We're thinking about spending a week or so in France next year, and will not have a car. Knowing the best regional hubs is very helpful. Thank you.

What about Bordeaux? I haven't been there, but did research it for a Covid-cancelled trip. It looks amazing, with tours to the wineries and good train access to beach towns and San Sebastian just over the border in Spain.

What a lovely dilemma-where shall I spend 6 days in France?!

6 days is a good amount of time. Without a car, I might suggest either Côte d'Azur or western Provence as these locations have much to see and excellent transportation options to explore. With 2-4 days and no car, I might look at the Loire Valley, Upper Normandy, Dijon/Beaune, or maybe Strasbourg.

Nice would be excellent. A car is more an annoyance than an asset there, and there is plenty to see and do for 6 days in that area.

Nîmes is also a good choice, with easy access to Arles, Avignon, Uzès, Pont du Gard, Aigues-Mortes and Montpellier.
Avignon has slightly better transportation links, but I find that there is more to do in Nîmes itself than in Avignon, and Nîmes has been "spruced up" in a way Avignon has not been (yet?).
Aix is less good, as you would rely in buses for almost all day trips.

Alsace (Strasbourg or Colmar) could work as well.

Bordeaux mentioned above: not so sure; 6 days would be too long. You need maybe 1 day in the city, 1-2 days for wine country depending on your level of interest, and 1 day for Arcachon if you wish - San Sebastián is definitely out of reach for a day trip.

What time of the year, by the way?

Avignon for sure, a centrally located transport hub, lots of half and full day minivan tours to sights in the area.

We would be there the first week of October

Ok, so anywhere in France is a reasonable choice at that time of the year. I would have avoided inland Provence in summer, and northern France in winter.

perhaps Dijon/Beaune? Beautiful wine country you can hike and bike

Nice is a great idea. Visit all the coastal towns on the riviera by local train: Villefranche (my favorite), Antibes, Menton, Monaco, and more. Lots of restaurant choices in Nice and even several Irish pubs.