so when being a FAA class 1 holder, could it be the case I am unable to obtain a JAA class 1 ?
That is POSSIBLE, it though must be said it is UNLIKELY. As we know all too well on this forum, aviation medical certification authorities in different parts of the world have minor differences of standards and emphasis. However, unless you are unlucky enough to fall foul of one of those quirks, then in general fit in one place is likely to be fit in most others !