You can swim in Arcachon, known for it’s bay. It’s not exactly the ocean, but you can take a little ferry to Cap Ferret at the other side of the bays inlet. We stayed there (also in September) close to Dune du Pilat, already some 30 years ago but looking around with google streetview much look still the same. I can remember as a vibrant but not overrun place.
The ocean in southern France is better known as the Bay of Biscay and known too for the high waves. So you can surf there too if that should be of interest, however far from spectacular like in California. I should not worry about the water temperature, it’s pleasant around that time of the year. And I prefer the climate of the ocean above that of the Mediterranean, maybe it has to do I live close to the North Sea.
However several years earlier I stayed in La Baule-Escoublac, west of Nantes, it has a kind of micro climate and very pleasant for swimming. And offers more variety for other activities than Arcachon to my opinion, so can be an option too.