Unfortunately, an Interrail ticket for dogs does not exist. Every railway company has their own policy.
Indeed, very different rules depending from country to country and operator.
I think if you can transport your pet in a basket, it’s usually free of charge with some exceptions or even bans on pets on trains in some countries. Bigger animals often need a supplement or kids ticket.
I think that you can buy these supplements mostly online or with the train manager.
The details for France (and TGV France-Spain) can be found here: https://www.sncf.com/en/passenger-offer/travel-for-everyone/pets
In FR this generally will mean half price of normal full fare and that will cost MUCH more as even a passday from a short duration pass.
ONLY if the beast is so small you can hold it in a container that is not larger as allowed luggage, you can take for free. IF asked for, you will also need to show all vaccinations etc.-and if not in container, it must be muzzled. FR has an old heritage of many yrs ago (that may wonder some in modern times) against rabies etc.
In FR this generally will mean half price of normal full fare
No it does not. Please read the information available at the link posted above.