You will be indeed not far from the Mediterranean sea, and it would be a shame not to dive there. But just south of Nimes it's not the better place to dive, as it is mostly sandy and with a bad visibility. You should rather go in the south west, closer to the Spanish border, or to the south east, in Marseilles area. Marseilles area is a very nice place to dive, with a lot a spectacular underwater landscape, and nice wrecks. Further in the east, you would have Cavalaire, a place known for its magnificent wrecks, and the best known place in France for Tek diving, with deep wreck and deep walls.
If I were you, I would go to Marseilles or nearby. As I live in Paris, it's 3 hours train from Marseilles, and I go there quite often.
From Nimes, it is something like 120km. You might also consider going in the west part of the bay of Marseilles, which is a little closer from Nimes. As an example, Carry le Rouet is 100 km from Nimes. I know from reputation a
dive shop in this small town. However, I never dived there myself. One advantage of this shop is that it also train in Padi system, and you should take care of going in a place used to padi system, as padi is not directly recognized by French diving legislation.
In October, providing there weren't strong winds before, you can expect a quite warm temperature of the sea : it might be around 20 °C or more at surface and the first meters, 16-18 later, colder deeper. I never had, even in winter or deep, colder than 13°, at 70m +. Last year, in early November, it was still at 16° at 60m depth.