To give you an idea what I'm talking about:
What I'm looking for is a PoD following Charlemagne's coronation in 800 and subsequent events that accomplishes three things:
1) Keeps Charlemagne's realm united, continuing to encompass pretty much all of Christian Western Continental Europe (so that it still looks essentially like the above map)
2) Sometime before 1000 at the absolute latest, unite the two "Roman" empires under a single monarch, or married monarchs (will essentially end up including the Papal states)
3) The newly reunited "Roman Empire" to remain united (including holding onto most of Christian, Non-Slavic, Continental Europe) for at least as long as the previous division lasted, or since 395*
And of course, how would these events and the "reborn" Empire change history?
*to give an example -- say, Charlemange and Irene of Athens marry in 820, then the "Roman Empire" stays more or less coherent, and cannot split in any lasting sense again until 1245; if the Empire is "reunited" in 895, then it would have to stay (again, more or less) so until 1395