You will only pay french tax, if you have a substantial amount of french -taxable income , such as bank interest , dividends, or UK State pension. This would be added to your police pension as I described , to make the calculation.
Here is an example using random figures ;
police pension - 20 000€ , state pension 8000€ , bank interest 1000€ …total 29000€ tax calculated ( this is this years figs. for a couple) …1344€ tax X 20000 /29000 = 927 credit. …1344 -927 = 417 - (decote…312)=105€ tax due before any other deductions like charity donations etc. This tax is in respect only of the 9000€ french taxable ( 1.17%). In addition there would be 17.5% social charge on the investments 1000 X 17.5% =164€ . If that9000€ had been the only income it would have been below the non - tax limit of 27531€ (couple), but including the police pension means that the 9000€ is taxed at the rate it would have born if all the income had been french taxable. Social charges are always due on investment income regardless of overall income.
The police pension is not taxed ; if it were the tax due would be 1344 - 1008 (decote) tax due…336€ .
( The decote is a device to reduce tax for “modest incomes” … they deduct 3/4 of the tax due from 1939€ (couple) and deduct the result from the tax.)