From Timatic,
Residents of France may enter using travel documents which are valid
on arrival.
This applies to holder of resident visa. For normal visa, the passport must be valid for 3 months from the date of departure.
See also: https://www.gov.uk/guidance/living-in-france
If you have rights under the Withdrawal Agreement, you can enter and
exit EU countries with a valid passport. You do not need any
additional validity on the passport beyond the dates on which you are
travelling.
tl;dr - You can enter with passport which is valid for less than 3 months, provided you have the resident visa.