MJ, you are incorrect. When an item is imported as piper boy boy did as a personal effect it is VAT exempt as its good and chatels. It is then deemed to be VAT paid.
I did this when I moved back to the UK with all of my personal possessions many ears ago.
The certificate of free circulation is nothing to do with it.
I would carry the notice of arrival as proof and ticking the VAT paid box on the GAR is perfectly acceptable.
The real issue is if flying in France how you convince the French Customs guys as they are quite blinkered at times. Notwithstanding this I have flown an N egg aircraft that does not have a certificate of free circulation and been ramp checked in France on a number of occasions without issue. Which does leave me wondering at times exactly how true the scar stories are about N reg and VAT.