Charlemagne was not so farsighted as to believe in the efficacy of a united Europe; rather he fought and worked to build a large and powerful Empire of his own, commonly known as the Carolingian empire. He was attempting to complete the empire which had been initiated by his father, Pepin the Short and his grandfather, Charles Martel. It was Martel who lent his name to the Empire, following his defeat of the Muslims at the Battle of Tours, which prevented further Islamic intrusions into Western Europe.
Charlemagne's association with all things Roman originates from the fact that he was crowned "Emperor of the Romans" on Christmas Day, 800 A.D. by Pope Leo III. There is some argument by historians that this was the beginning of the Holy Roman Empire, but there is no agreement on this point. It is more apparent that Charlemagne received the title in exchange for his having extricated the Pope from a difficult situation.
Bottom line, Charlemagne did not consider himself (nor has history considered him) as Roman in anything other than in name only after his coronation by the Pope.