The problem I have is twofold, 1. When filling out the GAR if I check the vat paid box, I am lying, if I check the NO box I,d imagine French customs would be on my back like a cheap suit. 2. If I get ramp checked and inform them no VAT was paid as under the UK scheme none was owed they could respond with "your not in the UK now so park it up till the Vat is paid"
Well the French wouldn't see the GAR form unless it was shared with them since there is no requirement to submit such a form when arriving into France or indeed any other EU country.
If you genuinely have no VAT liability for the aircraft then just tick yes to both VAT paid and free circulation on the GAR form.
Five years of flying various N-reg aircraft around Europe I have never actually been asked for proof of VAT payment/free circulation, perhaps I have just been lucky.