(To piperboy84) You wrote you hold dual nationalities. On your medical, does it state the 2 nationalities that you hold or just 1 nationality? And also, which class medical do you currently hold?
Cap, US&Uk citizen flying a N Reg on a FAA CPL ticket based in Scotland, FAA medical starts out at the highest class then drops down to the next class and I renew it every 2 years, can't remember the class designations but that's all really irrelevant. The only issue I have ever had flying on the continent was getting ramp checked to verify I had paid taxes (sales/import/customs etc) when bringing the plane over from the US, I had a waiver on the tax which the French customs cops at the airfield accepted after a bit back and forth.
To be honest I think you are way overthinking this thing, the sole deciding factor of which passport I use when entering the locals of foreigners line at an immigration check after getting of a commercial flight is whichever line is shortest and will allow me to get a Marlboro kindled up the quickest. As far as arriving on a GA flight my experience is nobody cares or checks your medical or even your license for that matter, as long as you have a current passport you're good to go ( I suppose a passport issued by North Korea or ISIS would raise eyebrows but from anywhere else is fine ) If you get ramp checked they seem to focus in on what country of registerey your aircraft has compared to what country address is on that registration and then cross reference that to the address listed on the insurance docs, again this is all about tax and not trying to see if your license or medical is current.