if your license doe not match the reg of the A/C (ie FAA & N reg OR G Reg & CAA) you would have to get consent from countries you visit
No. The airspace is not a lot to do with it.
The authority that determines what privileges (if any) a given license gives you on an aircraft is the "CAA" for the country of the aircraft registry.
So, on a G-reg, it is up to the CAA. The current ANO automatically validates all ICAO PPLs for a G-reg and this is good worldwide.
I don't think any other European country does this automatic validation for their own aircraft, and for such aircraft you have to get the non-matching license validated, e.g. by the French DGAC if flying an F-reg.