A car gives you ultimate flexibility on where you go and when (along with European gas prices, and sometomes highway tolls, and parking challenges). You could avoid different-country-return fees if you started in France, drove thru part of France on your way to Spain, then drove back thru another part of France on your return. Even if you didn't drive all the way to Paris, you could drop off the car someplace in France and get back to Paris by some other means. Or arrive in Paris and fly home from some other French city, like Marseille.
Some rental companies charge more for, or don't allow their car to be taken to, certain other countries. Might not affect you going between France and Spain, but make sure. If you need that car for more than 3 weeks, leasing is another option that could save you over renting.
Increasingly over the past few years, budget airlines (like Vueling) fly within Europe quickly and cheaply, and might give you another option for getting around. Of course, you don't see the country you're flying over so local people and culture at 30,000 feet would be limited, but it might get you to a specific place quickly where you could pick up a car and resume experiencing things up close. Some of those budget airlines have strict luggage policies, or can nickel and dime you with extra charges, so read the fine print, but if you decide you don't want or need that car the whole time, that might work for you.
You could also have a France car, turn it in and take a train or bus to a destination in Spain, then pick up your Spain car. Depending on the rental company, there could even be a charge for returning the car to a different city than where you picked it up, even in the same country, so again, read the fine print. Picking up a car at an airport or train station usually involves an extra charge, compared to picking it up at their location in town (if applicable), so that's another thing to possibly consider. Vacation time is valuable, though, so a relatively small additional cost for the convenience may be a good investment.
In addition to regular trains, France has super-fast TGV trains, and their counterpart in Spain are AVE trains. There are also fast highways and less-fast highways. Navigation by road signs often requires knowing cities in the direction you want to go, and following the signs for that location, rather than simply "following the A-90 then turning onto the N-236."