You are exempt as long as you are travelling with your EU spouse. Administrative formalities may apply if you stay in one country for more than 3 months consecutively.
The Practical Handbook for Border Guards, while not legally binding itself, represents the position of the European Commission on matters of interpretation on the Schengen Borders Code and other relevant Union laws.
On pages 20-21, section 2.1.2:
In the case of third-country nationals who are family members of EU, EEA and CH
citizens, they have the right of residence in a Member State for a period of up to
three months if they are in possession of a valid passport and are accompanying or
joining the EU, EEA or CH citizen, without any limitation to 90 days in a 180-day
To be noted that, third-country nationals who are family members of EU, EEA and
CH citizens are entitled to accompany or join the EU, EEA or CH citizen for
consecutive periods of up to three months per Schengen States without any
conditions or formalities (except the need to have a visa for third-country nationals
from a country subject to a visa requirement).
The previous stays performed in the area without internal border controls
accompanying or joining the EU, EEA or CH citizen should not be taken into
account for the sake of the calculation of the compliance with the 90/180-day rule
which is applicable to the short stay only.
and for examples it gives
An Indian national married to a French citizen may accompany his French spouse to
Germany for three months, Spain for two months and Italy for three months, thus staying
in the area without internal border controls for a total consecutive period of eight months.
A Japanese citizen is married with an Estonian citizen and has never come to the EU
before. The Japanese citizen accompanies his Estonian spouse to Italy for one month. Just
after that month, the Estonian spouse leaves Italy and returns to Japan to work. The
Japanese citizen can remain alone for another 90 days (the limit of 90 days in any 180-day
Stays over three months or establishing residence in one EU/EEA/CH country are of course allowed for a person staying together with their EU/EEA/CH spouse under freedom of movement, but the country may impose certain administrative formalities and conditions (e.g. applying for a residence permit).
For France, as it is the country of origin for your spouse, national rules may apply. But in any case, your wife has exercised her free movement rights in another (at the time) EU state (UK), so it shouldn't matter.