We have been discussing this in the corporate jet world...
If you fly an N registered aircraft, on a JAR licence you are allowed to do so only in the state of issue of that licence. ie if you have a UK CAA issued JAR licence you would indeed require an FAA ticket to fly to France.
Now then, let's say you now have your shiny new EASA licence. EASA member countries are technically a single state so in theory you can now fly an N registered aircraft in or between any EASA countries. No need for an FAA licence. (So long as the journey does not overfly a non EASA country)
I have asked several people about this (the CAA, several ATOs etc) and no one can give me a definitive answer in support of the above. The guy from the CAA just rubbed his chin thoughtfully and said "hmmm, possibly"!
I don't want to be the first person to have to explain this during a SAFA inspection though....