We were going to take the TGV when leaving Paris and pick up a car at the next station. However, after looking at the train time, it may as well just rent a car from Paris to save time and money.
We have decided to just rent a car from Paris to continue our trip heading south. Not sure which location to rent in order to avoid crazy driving and traffic within the city. Any suggestion?
We rented from Europcar on Ave Foch. If was on the 'other' side of the Arc de Triomphe (a quick walk from the metro stop by the arc) and easy to get to the ring road without having to go near the Arc. Mind you, we did rent on a Sun morning, so traffic was pretty light.
Since you are headed south, pick up your rental car at Orly. You'll avoid some of the Paris traffic madness.
We rented near Gare Montparnasse and got out fairly easily, though it was a bit of adventure. Orly would be easier. Or there are rental offices at Porte Maillot and La Defense on the western edge of Paris (right on the Metro), then take the Peripherique to whatever exit works for you.
We ended up taking a train to Reims and rented a car with Sixt. Super easy and convenient.