Others will no doubt be able to give you more detailed information but the basic rule so far as the French Tax Authorities are concerned is that if you spend more than 6 months plus 1 day in France in any calender year (the tax year runs from 01.01 to 31.12) you are classed as resident for french tax purposes. So spending less than that in France would mean that you wouldn't be liable under the basic rule.
That said, if your main home is in France and you spend more time there than anywhere else, I suspect you'd be regarded as as resident there. I strongly advise you to ask a local accountant-a 'comptable' for advice. Certainly people in employment in France pay significantly more tax than the UK though there are allowances for a spouse and any dependent children.
Good luck