Although only mentioned by the chronicler aristocrat of the Eastern Roman Empire Theophanes the Confessor, Irene of Athens (the ruling regent then Empress of the Eastern Roman Empire) had desired to arrange a marriage with the new Carolingian Empire's king and the so called Holy Roman Emperor, Charlemagne. For some reasons known and others unknown, this fell through, but had it not, a defacto Roman Empire would have been reborn. The old, arguably more legitimate Eastern Empire and the newly created Frankish Empire in the West, when made into one, would have been a massive power in Europe and the world stage. However, the problem of how the Franks dealt with royal lineage and inheritance, in which they split the land among the sons (when Charlemagne died the Frankish Empire was split three ways and quickly fell into war), would have to be dealt with in this scenario as reuniting and then disuniting the premiere Western Empire would make for boring alt-history and could/probably would have been dealt with.
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I can see this actually being a good video. Hopefully they adopt the Roman system of inheritance and learn there lesson from the Roman collapse.
It will not necessarily lead to the union between both empires. The division would already be too big to reunite them.