You need to go and have a look at the rule books and see if you can actually do what you intend to do.
You used to have to do the cpl in the country that you did your theory exms through. Then in theory you could add the IR in any Jar country you like.
But i suspect there maybe local regulations preventing you doing this.
The whole French converstion thing can be frought with paper work and regulations.
Your french ppl will have no problems in the uk.
Once you have all the legalities sorted out then come back for advise on schools. There are many good ones in the UK.