Renting a car

Get the train over the border to Perpignan, then rent there.
Unfortunately that means you miss the chance of taking the coast road from Figueres into France, which goes round the end of the Pyrenees, from Llança and Argelès-su-Mer. This is recommended.

We once rented a car from Hertz in Lisbon, Portugal and turned it in at Malaga, Spain. Because it was being returned in a different country and it would cost Hertz to return the car back to its origin, we were charged a very hefty second-country fee, but determined that it was worth the cost for the convenience. That's a case-by-case situation and others might have made a different decision. We've used Europcar many times with satisfaction, but never used them for a second-country drop off. You may find another company that will let you do it, but expect to be charged - a lot!

Another possibility, depending on where cars can be turned in and picked up, would be to rent in Spain, drive as close to the French border as possible and turn in your Spanish car there in Spain, then hop a train or bus into France, where you can pick up a French rental car.

En-route from Figueres to Perpignan, the trains that connect at Port Bou will see a portion of the scenery that drivers enjoy, but also more tunnels. (On Google maps, note the places where the train line goes straight but the road has switchbacks.) A hefty 2nd-country car drop-off fee is common for 2-country car rentals.

Laura, the "traditional" rail route from Figueres to Perpigna does follow the coast (with a lot of tunnels) via Llança and Argelès-su-Mer. But, the new high sped route stays inland and takes a straight line through the Pyrenees, with a long tunnel. You miss out on the scenery.

I find OpenStreetMap a lot clearer than Google, it shows rail lines and stations clearly, to find them in Google you need to zoom in and they are hard to read thin grey lines.