If you don't care to take the slower regular train, there is also another category of budget trains: Intercités 100% Éco.
It's generally within the same price range as Ouigo trains but without all the limitations around luggage and such, however like with Ouigo, you need to book tickets in advance online.
These are old style trains with a locomotive pulling coaches, the old regular "Corail" coaches have better seats that the Ouigo trains. On most lines these trains travel with a speed between 160 and 200kph, so not that slow.
The only downside is that's not always easy to find these trains in the SNCF trip planner to buy tickets.
https://www.sncf.com/en/passenger-offer/travel-on-a-budget/intercites-eco
I remember taking it once from Paris Est to Strasbourg but according to the SNCF website it seems like it doesn't exist anymore.