"Although the absence of any registration requirement means that most of us have avoided the bureaucracy involved in applying for a Carte de Séjour, there is a downside: it means that it isn’t always evident (a) how long we’ve been legally resident and (b) whether we have been properly exercising our free movement / treaty rights and are therefore ‘legally resident’. At the end of the transition period, from 1 January 2021, all British citizens living in the EU will need to justify their membership of the ‘protected group’ - those whose rights will be covered by the Withdrawal Agreement. Those of us living in France who don’t already hold a Carte de Séjour at that point could find ourselves at a disadvantage.
Going through the (relatively simple) procedure now of applying for a Carte de Séjour as an EU citizen will make sure that both of these things are done formally, in good time, and before it becomes necessary , so that after Brexit you can easily demonstrate that you are legally resident and hence can show that you are covered by the Withdrawal Agreement.
The draft Withdrawal Agreement provides in Article 17 that those already holding permanent residence cards (see below) will be able to exchange them for cards which verify our post-Brexit rights, thus avoiding potentially complicated and stressful administrative procedures."