The withdrawal agreement between the United Kingdom and the European Union provides for a transition period until 31 December 2020. During this period, UK nationals and members of their families already settled in France or wishing to move to France prior to 31 December 2020 will retain their rights as European citizens and will not be required to hold a residence permit.
Pursuant to this agreement, these UK nationals must apply for a new EU residence card after Brexit bearing the words "Withdrawal Agreement" before 1 July 2021.
UK nationals and members of their families who wish to settle in France and maintain EU residence after Brexit beginning after 31 December 2020 will have to request their residence permits as nationals of non-EU countries and must first obtain a long-stay visa D before going to the prefecture to submit an application for a residence permit.
http://invite.contacts-demarches.interieur.gouv.fr/BREXIT/Mise-a-jour-du-site-de-demande-de-titre-en-ligne-pour-les-ressortissants-britanniques-residant-en-FranceIf you are a UK citizen or the family member of a UK citizen and you have already applied for EU residency after Brexit via the no-deal Brexit website between October 2019 and January 2020, you do not need to make a new online application. Your application has already been taken into account and will be processed by the local prefecture before the obligation to hold a Brexit residence permit becomes enforceable.