I continue to pay tax in the UK, and do tax returns… But I am not resident, or tax resident - and don’t want to be!
And as a resident of France anything one leaves would be subject to French inheritance tax, even if English Law was specified for the distribution of assets.
I really see no benefits, even if I could. It could be different for people in other circumstances.
But the biggest possible dis-benefit to me could be that had I remained tax resident in the UK it could weaken my application to become a French citizen.