Good stop on fast train from Paris to Barcelona

Look up the following cities on Wikipedia and see if any suit your needs:
Perpignan, Narbonne, Beziers, Montpelier, Nimes, and Valence.

Figueres is worth a half-day (i.e. one night) if you want to appreciate the life and art of Dali. The handsome medieval city of Girona is worth a full day (two nights). But both are within an hour's ride from Barcelona on the fast train, not exactly midway points in your itinerary.

Marseille, Aix-en-Provence, Avignon, and Lyon are additional cities with direct TGV service to Barcelona.

Lyon is an obvious choice as France's second largest city and gastronomic center but it only shaves 2 hours off the trip so you were looking for something "half-way" it doesn't qualify. Features: Food, charming old town, museums, Roman theater and lit up city at night

Avignon is a little closer to half-way and is a small city at the center of Provence. A few days exploring the small towns of Provence might be a nice option quieter option between two cities. Features: charm, wine, Roman ruins and countryside

Nimes is pretty much halfway and offers sites in a bigger, busier town setting. I haven't been to Nimes but while it has ruins and parks and museums it has a reputation for being a more work-a-day town than a tourist center.

Whether that's better or worse for what you're looking for that's up to you.

Have a great trip!
=Tod