There is a tax treaty between France and the UK that allows tax paid in the uk to be claimed as tax credit in france.
https://www.impots.gouv.fr/international-particulier/questions/taxation-income-received-abroad
*If you are resident of France and have received income outside France, you must fill out return no. 2047.
However, in order to avoid double taxation, these income may qualify for a tax credit when of their consideration in France. According to this method, France, as the State of residence, taxes the entire foreign income (tax non-deducted foreigner), applying however in parallel, depending on the income concerned and the provisions of the convention, either a tax credit “equal to the amount of tax paid abroad” (A), or a credit tax “equal to the amount of French tax” (B).