France has published a handy checklist for converting FAA → EASA: https://www.ecologie.gouv.fr/titres-aeronautiques-etrangers
Direct PDF link
Local copy
Implementation of EU/US BASA (Bilateral Aviation Safety Agreement between the European Union and the United States of America) for pilots in France
1) Under the provisions of Regulation (EU) 2018/1139 European regulations apply to aircraft registered in a third country and operated by an aircraft operator established and residing or whose main establishment is located in European territory . On the basis of this text, private pilots holding an American license residing in Europe are therefore required to hold a European license and associated qualifications in accordance with Regulation (EU) 1178/2011, including to fly on aircraft registered in the USA ( aircraft N); conversely, pilots flying temporarily in Community airspace are not bound by this obligation.
However, the application of this obligation has been postponed until June 20, 2022 (see decree of May 3, 2021 published on May 8, 2021). Until that date, pilots holding an American license can therefore continue to fly on aircraft N in Europe.
2) Annex 3 on BASA licenses sets the conditions for mutual recognition of private pilot licenses issued by one of the Member States of the European Union and private pilot certificates issued by the FAA and certain associated qualifications.
3) Pilots holding an American license residing in Europe are informed:
a) that they can continue to fly on aircraft registered in the USA (N) until June 20, 2022;
b) that the theoretical and practical examinations required in accordance with the conditions laid down by the EU/US BASA agreement will be organized by the DSAC from 1 January 2022;
c) that the DSAC will issue licenses and associated qualifications, in accordance with European regulations, on the basis of the conditions laid down by the EU/US BASA agreement from 1 January 2022;
d) that, until June 20, 2022, US licenses may continue to be validated according to national procedures, for pilots wishing to fly on aircraft registered F;
e) that pilots who already hold a European licence, but who have kept their valid US instrument flight rating, can already, and are even encouraged, for those who will need it after June 20, 2022, to convert it to IR (A) European according to the provisions of appendix I “Part FCL”, appendix 6Abis, point 8 of regulation 1178/2011 still applicable.
4) the guide concerning the conversion of ICAO licenses for ATOs and DTOs will be updated soon to add a description of the provisions of the BASA and provide explanations on the training provided for by the agreement
So, France is saying they will not extend the derogation beyond June 2022.