The answer to this would probably lie in the French "ANO" - does it prohibit what the UK calls "aerial work" in non F-reg aircraft?
If a French instructor takes his student into UK airspace, in an F-reg, and is paid for the instruction (which "obviously" he normally would be) then he is breaching UK ANO Article 140.
I am not aware of such a prohibition in France but then I would hardly know if there was one.
Like many, I had an instructional flight in a G-reg (the old "cross channel checkout") to LTQ with an instructor who obviously got paid for it. Thousands of these have been done so I guess that if they were illegal
in France it would have surfaced by now.
IMHO they are certainly not illegal as far as the CAA is concerned. I am not aware of any territorial restriction on loggable UK training flights.
The other angle is this: would the French know? It's just another flight from the UK. The instructor on board is hardly going to advertise his presence. Historically, loads of training has been done outside UK airspace, precisely to avoid the Art 140 restriction on training in say N-reg
