There is an instance reserved for French civil servants but as the product is open source under MIT license, some companies host it for private clients.
There actually is an open-source form system already: Démarches Simplifiées https://github.com/demarches-simplifiees/demarches-simplifie.... It's maintained by the French government and used by hundreds of administrations. Totally agree that Cerfa would benefit from being open too
We can cite https://mosa.cloud/ for instance