That's a very interesting and hotly debated question. Charlemagne was coronated the emperor of Rome. Pope Leo had to flee Rome due to conflicts with the population of the city. He asked Charlemagne for support and the king returned with the pope to Rome.

The sources we have on the subject are very sparse and they are mainly from an outsider perspective. What we can gather from these texts is that he was coronated Emperor of the Romans (cf. „Vita Leonis tertii" in „Liber Pontificalis"). The sources agree that the "normal" procedure of a coronation was followed: 1. The coronation, 2. the acclamation of the people, 3. the anointment. The texts make no reference to territorial claims of the emperor.

The idea of the translatio imperii, the translation of the empire, i.e. the understanding the Roman empire was passed upon the Holy Roman Empire was developed later. Late 9th century-12 th century by Otto von Freising.

The coronation of Charlemagne as emperor was more important for the pope than for the emperor himself. To be sure: His reign was extended to city of Rome formally, but it was the Papacy whose authority was immensely strengthened.

It’s important to remember what ‘Roman’ means in the eighth and ninth centuries in the Latin West. Roman citizenship and ethnic identity had long since disappeared, replaced with a concept of the Roman Empire bound up with Christendom, an understanding in the West increasingly centered on the papacy. The claim to the title of emperor by Charlemagne was not a claim to rule over all those considered Romans or all lands that had at one point or another been ruled by Rome, but a claim of divinely appointed authority over the Christian community, rooted in models of imperial and religious rule associated with Rome. The coronation in that sense can be read as a rejection of Eastern Roman imperial and religious authority over the West and the Holy See (Rome had long been within Constantinople’s sphere of influence). Instead Charlemagne as emperor could take up the mantle of the good Christian emperor on the order of Constantine and David. Post-Roman associations with imperial/religious traditions were not new. Reccared, the Visigothic king of Spain, was praised as a new Constantine for his decision to return Spain to the true Catholic faith.

Perhaps most telling of the transfer of authority that was about to take placed occurred a few weeks before the coronation. While in Rome, Charlemagne received envoys from the Patriarch of Jerusalem, who delivered to whom the keys to the city and to the Holy Sepulchre. The symbolic gesture might suggest foreknowledge of the coronation, and implies the submission of the patriarchal see to Charlemagne rather than Constantinople, whose emperors had formerly been recognized by Jerusalem as the secular leaders of the Christian world.

While Charlemagne was crowned Imperator Romanorum (emperor of the Romans), the formula was soon changed to Romanum gubernans Imperium (governing the Roman Empire). The distinction is significant. In terms of Frankish identity, Romans were the inhabitants of Rome or those that utilized Roman law codes, e.g. the Aquitanians, not a useful demonym to describe all those who inhabited the former lands of the western Empire. The latter is more amenable to evolving conceptions of Christian rule and identity in Western thought, tying re-definitions of what it meant to be Roman with models of secular Christian authority rooted in an imperial tradition.