Hi Nigel, I do exactly this.
PM me next week (I am away at present) and I will send you the correspondence I received from French DGAC - which I now carry in my flight bag just in case.
Essentially, no issue to fly in France on ICAO license (FAA) on G reg aircraft, as long as you are not flying in IMC or commercially (same as our ANO). The French would have issue (strangely) if you flew a F reg machine.
I suspect the rest of Europe doesn't care that much (but happy to contact their aviation authorities when required).