The laws are currently being revised in particular with regard to financial affairs, the Archdeaconry has been holding a series of meetings to update chaplaincies in France. You can read summaries of these meetings on this page
Anglican churches in France follow Diocesan regulations, but also need to comply with French law.
Each chaplaincy is responsible for making sure that it is not contravening French law.
The Association 1901 status is a non-profit organisation. A 1905 Association is a religious organisation, but you have to have the 1901 status first.
The association Actes6 provides a lot of useful documentation for churches in France