Yes-INTernat. TGV just have gotten some fancy name-and a much higher supplmt to pay if you go OVER border-but for domestic its just a normal TGV. However-there is a high chance that the quota for passholders is much earlier ´epuisé=taken´ as in other local TGV.

I am not sure if I got you right So you think, the One Country Pass is valid on the TGV Lyria?

 To check whether a train is usable you simply use the Interrail find train times or planner tools. They will show you the trains covering your journey and if they are not valid it will say so.

The TGV Ltria is showing as needing a reservation but is usable with your pass from Mulhouse (France) to Paris,