Exploring what Charlemagne was trying to accomplish for the empire
For Charlemagne amassing an even larger kingdom would help restore the Holy Roman Empire to the glory that it had known during the time of ancient Rome. Much like Justinian with the Byzantine empire, Charlemagne has aspirations of reasserting the Roman empire as it had been understood before its fall. He was successful in uniting the Church and the state and creating the potential for a "new Rome" when he was crowned "Emperor of the Romans" by Pope Leo III.
We can see evidence of Charlemagne's intentions through the Crusades. The Crusades led to the "forcible conversion" of Saxons, Lombards and Slavic peoples. The spread of Christianity was definitely on Charlemagne's mind when he authorized the Crusades; unlike the Muslim "jihads," however, the Crusades were intended to recover territory rather than converting pagans (Fiero, 2002, p. 84). It would seem that from the outset the Crusades were less about spreading the Christian doctrine than gaining material power.
Why do you think that both of these powerful kings, instead of establishing a new empire, wanted to restore the Roman empire? What about the Romans would appeal to these newer civilizations and cultures? What about the Roman culture was worthy of restoring? Why did the Roman empire continue to have such an influence?