In existing areas where France requires age checks, such as adult sites, they require sites to offer doubly anonymous verification. In doubly anonymous verification the site does not learn the user's identity, and the site that actually does the age check does not know which site the check is for.

Furthermore, France is in the EU. They expect to deploy their implementation of the EU Digital Identity Wallet by the end of 2026.

That allows users do age verification using protocol between the user's smart phone and the site with the age restriction. (Later they are expected to add support for smart cards and security tokens like YubiKey so a smart phone won't be required).

That system works by storing signed identity credentials tied to a hardware security device you provide, and using a zero-knowledge proof based protocol between your device and the site to prove to the site that your identity credentials show an acceptable age without providing any other information to the site.

The EU has been working on this for several years, and it is currently undergoing large scale field trials.