Since 1 January 2021 and the entry into force of the Brexit agreement, British citizens who wish to start a business in France must comply with new rules.
You lived in France before 1 January 2021
Until 30 September 2021, British citizens who lived in France before 1 January 2021 do not need to obtain a residence permit to live in France or a work permit to carry out a professional activity.
Consequently, you may start a business in France without a residence permit until this date.
From 1 October 2021, holding this permit will be mandatory. A specific "Brexit" residence permit must be requested before 1 July 2021.
You did not live in France before 1 January 2021
British citizens who did not live in France before 1 January 2021 must obtain a residence permit to start a business in France. Residence permit requests must be made in the relevant prefecture.