Yes it is included. You need to add a 37€ seat reservation (one of the most expensive high-speed trains). This route is very popular so you need to book well in advance. Some dates in July are already sold out.

Alternative : longer but cheaper and more scenic (coastal route). Here is a good schedule example :

Barcelona-Passeig de Gracia (Sants station at 11:16) - Portbou 11:21 - 13:56

Portbou - Montpellier St-Roch 14:26 - 17:09

Montpellier St-Roch - Paris Gare de Lyon 17:50 - 21:18 10-20€

TGV Inoui in France require a seat reservation : limited 10€ fare, then 20€ until the train is full. You can book them here : https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish (4€ booking fee per order compared to 2€ per person per train on interrail.eu)

Btw as you live in the UK you need an Interrail Pass

Thanks for your reply.

May I know, does  37€ is a standard price for seat reservation in TGV INOUI regardless of my destination?

Besides, why do I need to obtain interrail? Because I am a non-UK and non-EU citizen, and as far as I know, interrail can only be used by EU citizens.

Thanks 

37€ is the seat reservation cost for Barcelona - Paris only (27€ Barcelona - southern France). TGVs to Switzerland and Italy also cost around 30€ but the former can easily be avoided by taking a TGV only within France to Strasbourg or Mulhouse (then reservation-free regional train across the border)

Otherwise all TGVs within France cost a limited 10€ fare and then 20€ until the train is full.

You should choose the Interrail pass as it is the country of residence (COR) that matters but in fact nobody will check your COR as long as you show a non-European passport when asked. Interrail passes have a 2-day limitation in your COR while there is obviously no such things for Eurail.