Essentially, yes, as the spouse of a French person (and EU citizen) you have the right to live in France.
This is set out in both French and EU law.
However, even so, it is expected that British spouses of French people will still have to apply for a “Brexit deal” residency card before the cut-off date, which is currently June 30, 2021.
These cards are intended to be tailored to the situation of Britons already living in the EU and aim to allow you to “continue your life as before” with much the same rights as an EU citizen.
All third country citizens in France need some form of carte de séjour, so if it was not the Brexit deal one, then you might have to apply for a third country citizen’s “private and family life” card instead.
Send your queries about life in France by email to firstname.lastname@example.org