One week in France, two days in Nimes, Where else?

I'd take a train (as little as 3 hr. 32 min.) to Nimes rather than driving. ViaMichelin estimates the driving time at 7 hr. 26 min. by the fastest route, and that doesn't include stopping, traffic tie-ups, navigational errors, looking for parking, or time spent dealing with the rental agency. That's way too far to drive after an overnight flight. Alternatively, you could look into flying into Marseille, which would leave you with a much shorter rail connection.

Nimes is near the western edge of Provence, a part of France extremely popular with tourists.

When is your trip?

The drive from Paris to Nîmes is very long, traffic-prone in the second half, and not that interesting. The train is a far better option, plus you do not really need a car in Nîmes - it is easy to visit Nîmes itself, Pont du Gard, Uzès, Arles, Avignon, Montpellier... all by public transport.
You might still like to have a car to visit more of the region after your concerts, it will be useful to go anywhere east of Avignon.

Nîmes has a TGV station, so don't bother with a car. It's a looong drive that wastes your precious time. From Nîmes you can take a local train or bus to Montpellier, Sète, Marseille, Avignon, Arles, Aiguë Morts. Rent a car for La Camargue, Uzès, Aix-en-Provence. Uzès does have bus service to Nîmes but it's slow. A day trip could be Nîmes to Uzès over the smaller roads, over to Pont du Gard and back to Nîmes. Avignon is right around there, too, but deserves more time.

Or take the train down to Nîmes, and then rent a car to have when you are there. The best of both worlds.

Nîmes is a beautiful city. Great choice. Avignon is a train hub and also a great town. You can pick a hub and drive or take the train to many towns in Provence. I would also hit Lyon on the way back.