Sue, your statement about the first trip to France suggests that this is not your first trip to Europe. Is that correct? I ask because it sounds like you will be leaving your luggage in the car a lot, which is both risky and inconsistent with having the smallest car you can find. If you haven't bought a Rick Steves France book yet, you can read his general travel tips in the library, or (top left, desktop site) many of them for free-I mean trains and driving. Actually, for the route you describe, you need Lonely Planet France, not Rick Steves. But he is perfect for first-time Euro travelers.
I think that what we're trying to say is that your selection of endpoints means that you have a lot of banal driving past forgettable places. I don't mean you have to see only the high points on your first trip to France; I've been there at least eight times. But have you even pulled up Google Maps to see the length of the drive? France has perfectly good highways, there's no reason you can't do this if you want to apply an "American" Interstate Highway sensiblity to your first trip to France. But it may not be the best use of your time and money. A car is useful for many things in Europe. You have not made a case for needing a mighty steel steed of American freedom on your particular mission!
It is a tremendous liability to have a car in Paris. I drove to New York City every day for 20 years, and I will NEVER drive in Paris again after I stupidly arranged to return our car "downtown."
Just to start the idea (not to say it's best "for you"), consider an open-jaw flight Texas/Brussels and Paris/Texas. Train from Brussels to Tournai, very short train to Lille, where you rent the car in the same country you're going to return it, just outside Paris, perhaps at the airport even though you're going into the city for three nights. Even better (because the connections are so good), train from Lille to Paris, and go to another desirable city by train, where you rent the car. I mean like Tours, Lyon, Carcassonne, Limoges, Orleans, or even Bordeaux - depending on your interests. By interests I mean .... wine, history, cider, dead princesses, religious history, chateaux, expensive restaurants, World War II, whatever.