Without disagreeing with the thrust of what has been said, there is no "two out of three" rule. This is general guidance to help pilots remember the basics behind a more complex set of rules and guidance.
For flights with JAR-land, there should be no issue with an FAA PPL flying a JAR-registered aircraft under day VFR wherever he pleases, irrespective of borders.
The French are traditionally slightly awkward around this subject, not because of any deep-seated convictions, but because the guys typically doing the ramp checks are the local gendarmerie who have a very variable understanding of the documents that they are asking you to produce. The Dutch, German and Belgian ramp-checkers are less likely to ask for your paperwork, but are rather more educated when they do.
Secondly, in response to whose rules do you obey, the short answer is all. FAA, country of aircraft Reg and country in which flight is conducted. Apply the most restrictive rules applicable in the case of conflict.