Hi,
see here the conditions , when you are a French Tax resident ( so here you have to take some precautions if you want to avoid having to declare your world income, and the taxes paid in France too):
Impôt sur le revenu : notion de résidence fiscale
Notwithstanding, when you have a house in France, the Tax Office can tax you on a 3 times the effective renting value of your house.
However the above possbility is usually used for people who have very high total estate, and who attempt to avoid paying taxes in France. A last resort, you can not oppose.
A point you will also have to consider, any from housing will be subject to the French succession rules, which are very different from the GB rules.
And a GB will for this will be void. So you need to organise the French succession, to reach or try to reach ( not always possible ) what you really wish. The more children you have, especially from different marriages, the more complicated it gets.
You have to consider this on how you purchase a housing - it can save quite some money, instead of having to adpat later.
Yours,
giantpanda