If that is the French position, transfer your CPL licence to the country where you are doing the FI rating while you are resident there.
When you have the CPL with FI rating, transfer it back to France if you are going to work there or the UK (if you want) if going to work there.
The UK is an "odd" (for want of a better word) place. Everyone rushes to specify that they have a UK Jar licence rather than simply a JAR licence and as the Prime Minister said in Parliment they very much try to have British jobs for British people even if it is illegal.
That is why many people recomend that you do the course in the UK if you want to work there.
Regards,
DFC