The "Holy Roman Empire" came about by the Roman Empire co-opting Christianity, which had made serious inroads, and threatened the Roman Empire, which was wrought with wars, hedonism, a poly theistic religion, decadence etc etc. In the co-opting of Christianity, who, at first they persecuted fiercely, the merged the two together, while retaining the trappings of their earlier 'pagan' religion.
Hence, they created a Theocracy...where the Pope replaced Caesar as the sitting head.

You appear to be confused between the adoption of Christianity by Constantine, and its establishment as state religion by later emperors (around 360-450CE) and the (originally Frankish, later mostly Germanic) Holy Roman Empire started nominally by Charlemagne about 400 years later. Of which it has been said, was neither holy nor Roman, and scarcely an empire. The Pope was never head, even in title, of either the Roman Empire or the Holy Roman Empire.