Suggestion
Could 'cabbotage' be an issue here?
It may be that it would be perfectly legitimate for a UK based instructor in a 'G' registered aircraft to take a student on a training flight through French, or any other, airspace provided that the flight either commences or finishes at a UK aerodrome.
By contrast, it would definitely be illegal for the same instructor to base himself and his 'G' registered aircraft in France and then carry out training flights commencing and finishing at a French aerodrome, even if his students were resident in France.
Broomstick.