Thanks folks for the speedy replies. Just to clarify futrther, the aircraft (a Grumman Tiger) has a full C of A, is on an SDMP and I have a class 2 medical vailid until March (and an LAPL medical until March the following year, which would allow me to fly on my PPL reduced to the privileges of an LAPL if ncessary).
Putting the aircraft on the French register after the end of this year would be a lot more difficult than while we are in EASA.. As long as we are in the EASA, it is a (very) administrative process but involves no inspections or regulatory complications... just basically moving the paperwork from one country to another.