“Very early on, we took strong measures to protect the French public. But everyone knows, and we have to say it transparently: These measures come at a cost to our public finances,” Ms. Borne said in justification of the less generous caps. In total, the government’s capping measures next year are expected to cost €16 billion, Finance Minister Bruno Le Maire said at the conference, with €11 billion going toward gas and €5 billion on electricity."
So I would say that the French govt. directly subsidizes this price regulation