It is regulated by the state through an agency, and all players have right to vote for or against a charge modification
Though, taken with extreme amounts of salt, rumors are that the regime, along with Spain's, are illegal against EU law.
CallumC.Gurney, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons. Map of services running with Corail stock in France.
Oxygènes units have been ordered to run all the day Intercités services left running on Corail stock, i.e Bordeaux-Marseille, Paris-Clermont-Ferrand and POLT (Paris Orléans Limoges Toulouse) line services (in Orange on the map)
That isn't how that works
I knowingly skip the fact that SNCF {Voyageurs, Réseau...} are controlled by the French State, just stating the legal facts.
Any stock working Intercités service are owned by the French state in its own capacity, and only operated by a legally separate operator, SNCF Voyageurs, a private company. If the tender for a particular service goes to someone else, the stock will go to that operator (like TER services).
If SNCF Voyageurs wants to run open-access TGV services, as all TGV services run without subsidy, they can (not that they will, again there is a shortage of TGV units that it seems SNCF Voyageurs don't want to fix for whatever stupid reason), and that won't impact the tendered contract they will likely hold to run the IC service on behalf of the French state.
On top of that, quite plausible, rumors are that the French Gov wants to privatise IC services (likely as a coverup of the unwillingness and the underinvestment on the classic lines), and that SNCF Voyageurs is likely to not even tender to the night IC with the new stock (as we already knew that SNCF doesn't want to deal with night trains in the slightest).