The State only offers free language training in limited circumstances. This is currently aimed at non EU/EEA citizens who have moved to France and have poor French, and only if they are refugees or have a type of residency permit that requires them to sign a Contrat d’Accueil et d’Intégration, which includes a commitment to achieving a certain competency in French.
This includes those on workers’ residency permits or applying for a long-term resident permit after five years in France. This would apply to Britons coming after the transition period, if they fall into a qualifying category.
Even so, you may be able to join one of the courses on a paying basis and you can search for language learning providers
If you are planning to move to Paris, check here for paying French language courses
If you are a registered jobseeker, Pôle Emploi may also fund free French language training (Pôle Emploi has its own database of courses).
Also both jobseekers on unemployment benefit and workers now accrue training points each year in a personal Compte Formation that can be used towards paying for a language course.
There are many other ways to access FLE (français langue étrangère – French as a foreign language) courses, some subsidised by local authorities such as mairies and regional councils, and it is worth enquiring at your mairie or a cultural centre. You may have to pay a modest annual subscription in addition to a token amount for lessons, and to pay for notebooks, textbooks and dictionaries.
You may also wish to do a search on maformation.fr a resource listing adult education courses (however many are limited to workers and jobseekers) or check the site of your local greta. The latter are groupings of adult education providers (eg. try a search with ‘greta’ plus the name of your geographical department).
An internet search for FLE gratuit (free FLE) brings up useful sites for learning at home such as courses by state TV channel 5 at apprendre.tv5monde.com/fr or bonjourdefrance.com. There is also bbc.co.uk/languages/french
See also national distance learning body cned.fr, or visit mooc.afpa.fr for courses run by a national training body Afpa (it has an ongoing free FLE course that has begun, but which you can still join, or look out for future ones).
Finally, here is a directory of language schools offering FLE.
If you know a useful free French learning website please share details of it via firstname.lastname@example.org