UK Tax restriction
Coming to stay or simply visit for working flights whilst living abroad?
An individual Not Resident and Not Ordinarily Resident for UK tax purposes will have a potential UK tax liability in respect of UK Income and remuneration in respect of UK duties as an employee.
(nb Subject of potential Capital Gains tax should not be overlooked but I am ignoring it for the purpose of restricting length of this response).
So will you continue to reside abroad within visit limitations perhaps as a French tax resident working for a UK based company?
If so, you could find yourself only having to report say 5-10% of salary depending on actual rosters for UK tax purposes and still claiming full UK tax free allowances to offset.
Understand that UK/ French DTA hands prime taxing right to UK when working for UK based company and French still interpret DTA from their side as not to tax difference, although that has been subject to potential review for some while now and latest French position best checked out with French tax advisor.
If you become regarded as Resident and Ordinarily for UK tax purposes then full UK taxation on employment income for duties of employment exercised partly in and out of UK.
Non Domicile claim unlikely to help mitigate tax on such employment income.
Hope that this is of some additional help.