Seat reservations are optional on most European trains. As Brendan said, you can get them for free in most countries.
However this is not the case on high-speed trains in France, Italy and some cross-border routes (+ pretty much all Spanish trains) : you need a seat reservation, otherwise you won't be allowed to board.
General advice for seat reservations :
https://community.eurail.com/train-connections-reservations-47/how-to-get-reservations-105
https://www.seat61.com/interrail-and-eurail-reservations.htm
The TGV between Barcelona and France is very popular so you need to book well in advance. It has one of the most expensive seat reservations unfortunately but regular tickets often cost 200€ (so the pass is still good value)...
To save money (but not time) you can take the coastal route via Portbou to Perpignan, Narbonne or Montpellier. Fully reservation-free. From either city take a TGV to Lyon (in both classes : limited 10€ fare, then 20€ until the train is full).
Book TGVs within France here (clearer overview, less booking fee) : https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish