Probably not as a single, cohesive, continuous state but look at something like Imperial China which saw itself as a 2000 year old state but had gone through various dynasties and periods of territorial disunity. Similarly, Frankland could have gone through various stages of territorial acquisitions and contraction and even temporary splits but could still be, now, a unified country.
To answer your first point, yes but Europe isn't China. China had special circumstances which allowed it to remain a cohesive unit, and some might argue that logic and chance should have conspired to make it break up at some point, to a far greater degree than ever happened in OTL.
To answer your second point, true, that simply wasn't what was originally implied. It's unlikely, but possible.