With Charlemagne's coronation as Holy Roman Emperor, the placement of political power shifted. Whereas formerly power had rested with Rome and the Romans, it moved with Charlemagne to the north of Europe and to the Teutonic peoples of his Empire, thus creating a new political power center.
Charlemagne believed in bannum. This was the type of system which gave him the right to rule the areas by which he commanded. His political system was based upon the hope that the people under his control would support him.
Charlemagne is a perfect example of how one forceful personality with plenty of charisma can be the glue that binds together a powerful and large empire. Without the power of his personality, as other editors have noted, his empire would probably not have existed in the first place.
Charlemagne ruled over, not necessarily through, local officials known as counts among the Franks, and their equivalents in places like Lombardy and elsewhere. He sent bureaucrats known as missi dominici armed with decrees called capitularies in order to try to attain some sort of legal uniformity and project his power. The system of feudalism, however, was not really in effect yet, at least not the pattern of mutual bonds based on land and military service. Ultimately, Charlemagne ruled over his counts, and indeed financed his court through booty acquired through military conquest and tribute exacted from conquered peoples.
His empire had a feudal system that was essentially only held together by his personal characteristics. The empire did not even have a system of taxation to support Charlemagne and his government. Instead, the king had his own estates and used the revenue from them to support him. The nobility would each be in charge of their own little fiefs. So it was very much a feudal system rather than any kind of a modern governmental system (or even a system like the Romans had).