You are liable to UK tax on income earned in this country, regardless of where you live. You may also be liable to French tax if you are resident there under French tax laws. There are, however, Double Taxation agreements which ensure you do not pay tax twice, but usually end up paying whichever is the higher rate in the 2 countries. As a general rule, you pay National Insurance contributions in the EU country you work in, but these are both complicated areas that you need to take specialist advice on.