It’s possible to buy a passholder reservation for TGV from Paris to Barcelona here: Vos billets de train & bus en Europe - Réservation sécurisée avec Rail Europe

Oh I should have mentioned that I will be in Lyon. 

But actually going to Paris and then to Barcelona is a possibility… Not the most straightforward I would say.

Just for the spanish AVE it is not possible to reserve it from any other place then Spain itself. 

But it would be possible to go from Lyon to e.g. Valence TGV and board the TGV from Paris to Barcelona there. That’s possible, too.

It’s possible to try to buy a reservation on the train from the conductor at the day of travel but it’s a little bit risky, too.

A Spanish ticket office can sell the reservation, the difficulty will be that they usually want to see the interrail pass before they will issue it, if you have someone who can go it is certainly worth a try though.

It is also possible to buy on the day from the train staff but obviously there is no guarantee of seat availability.

If you live in or near Lyon you could go to Part-Dieu station any day and speak to RENFE staff on the platform (last time I used the AVE the ticket barriers were not activated) at around 1-2pm.

I don't know if they can sell reservations for later dates but it's worth to try! Feedback very welcome.

You can access more details about seat reservations by visiting this link: 

https://www.seat61.com/trains-and-routes/paris-to-barcelona-by-train.htm