I don't see why you couldn't fly a G-reg on an FAA license, regardless of the country you fly in.
It's not the country you're overflying that says what license you need to fly the aircraft; it's the country that has registered the aircraft that decides what is needed to fly it.
And of course the ANO is just UK law, but it's all that's needed. My guess is that you'll find (in other countries' legislations) things along the lines of "foreign registered aircraft are to be operated in accordance with the rules of the country registering the aircraft"...
Look at it this way: you can fly a G-reg with a national UK license (not JAR) without any problem in Europe.
From a French/German/Whatever perspective, an FAA certificate is no different than a national UK license; it's just a non-French/German/Whatever license... so why should it be treated differently?