The Byzantine Empire (or Eastern Roman Empire) was the powerful and ancient Eastern counterpart of the later German "Holy Roman Empire". But unlike the "German Kingdom", as the Romaioi called it, Byzantium was actually an unbroken extension of the old Roman Empire, unlike its Western imitator. When the HRE came about in AD 962, Byzantium was already 600 years old and it was still a powerful and lively relic of Late antiquity.

The Byzantines reached their second zenith in AD1025 under Emperor Basil II, and had another golden century under the Komnenoi from AD 1081 to 1180. However, in AD 1204, Constantinople was sacked by Latin Crusaders and this event severely crippled the Empire's political, military, and economic power. Despite this, the Byzantines managed to recapture their capital and persist for another 200 years until, when, in AD 1453, the Ottomans extinguished the flame of the Empire for good.

The Byzantine Empire.

But, keep in mind that in the high/late middle ages, the notion of national power is a bit tricky. The HRE looked powerful on paper, but in reality it's Emperor did not hold that sort of Imperial power that a Roman or Byzantine emperor had. Likewise, the French and English kingdoms had varying states of power over its de jure territories. Ah, the joys of feudalism.