Residential and tax status
If you plan to live 183 days per year or more in France, you will be officially fiscally resident in France. You will thus become a full French taxpayer, as regards income. This concerns your income wherever it may be - including pensions, dividends, unearned income or earned income of any sort. You will not necessarily be worse off in France, unless you have a very high income. If you have a low income, your income tax in France is liable to be less than in the UK. Half the population of France pay no "income tax" at all. However, French "income tax" does not include the additional "CSG" and "CRDS" taxes, which in everything but in name constitute a virtually flat rate income tax, currently amounting to 11% on all income.
If you are fiscally resident in France, you will also be subject to French jurisdiction in the event of death. Your estate, including all assets in any other country except property , must be divided up among your heirs in compliance with French inheritance laws, which impose an equal distribution among your direct heirs (children) of the major part of your estate - two thirds of it if you have two direct heirs, three quarters if you have three, etc.. It is impossible, under French law, to leave all your estate to one child, and none to another - whatever mitigating circumstances there may be. As for leaving it all to a home for stray pussy cats, you can only do that if you have no direct heirs at all.
As a resident with an EU nationality, you can vote in municipal elections and European elections. You can also be elected to the local council, but you cannot become mayor.