FAA Multi Rating UK
I suggest contacting Baudouin at Orbifly.
He can do your training in France and you can use your own aircraft.
He will also arrange the flight test.
Very straight forward procedure.
If you wish to do it in the UK then you simply need to find an FAA CFI/MEI and obtain DFT approval to train in your aircraft.
Again relatively straightforward.
You would still probably have to fly to Le-Touquet to carry out the flight test.
Hope that helps.
PS I have personally been through both of the procedures above.