Did Charlemagne’s empire represent a rebirth of civilization in Western Europe? to what extent was it Roman culture and to what extent was it something new or different?
By the time of Charlemagne, the Western Roman Empire had descended to isolated kingdoms with no unifying identity or central authority. Charlemagne unified the part of Europe that he gained control over, giving it a new identity and center of control. It can not be said that this process was a "rebirth" of the former Western Roman Empire. By contrast, the Eastern Roman Empire in Constantinople was still a unified empire that carried on into later centuries.
I, too, would not call Charlemagne's rule as a rebirth of the Roman Empire. Instead, I would agree with the others posters by stating that it was more of an enlightenment (in regards to culture). He wished to illuminate the importance of art, culture, and religion.
I don't know if it is necessarily the most accurate phrase to use in describing Charlemagne's rule as a "re-birth." You need to be able to justify such a phrase based on what came before and after in terms of the historical context. Whilst his empire and rule clearly resulted in a significant cultural and military "flowering," at the same time I think that calling this a re-birth would be a slight exaggeration.
Hopefully, Charlemagne planned to learn from the mistakes of the Roman Empire. The biggest mistake was that the empire got too big, and could no longer defend its vast holdings. Charlemagne might have had some of the same land, but his empire was much smaller.
It seems that most people do not like the idea of a rebirth. Let me play devil's advocate here. In some ways, we can see the reign of Charlemagne as a rebirth, because his rule is associated with the Carolingian Renaissance. There was a revival of art, religion and culture during this time. Also Charlemagne also defined his empire in terms of geographical area.
Charlamagne has long been celebrated as a ruler who took a genuine and personal interest in learning and in "culture" -- a commendable trait in a person who might simply have been interested in political power, military might, and personal self-indulgence. To the extent that he nurtured and inspired such an interest in others, he deserves the praise he is often accorded.
The Roman culture of antiquity had disappeared completely by the time of Charlemagne. He may have ruled over what was once Gaul and the Rhine, but politically and economically it was not the same entity as it had been under the Roman Empire. He may have borrowed the "trappings" of political power in the Roman fashion and may have started lineage for the rule of Western Europe that endured a thousand years, but it can hardly be argued to have been a "rebirth" -- it's a hard enough argument to claim that he even "maintained" the Empire.
Contrasted with the Eastern Empire, which continued to be politically and economically vibrant for centuries, Charlemagne incorporated Roman forms that gave the West some cohesiveness for a few generations.
It also does not seem right to talk about Charlemagne's empire as a "rebirth of civilization." That sounds more like the way historians conceived of things a generation or so ago when we still talked about the "Dark Ages." That view makes it sound as if civilization completely disappeared after the "fall" of Rome. People in those days would not have seen it that way and most historians don't look at it that way now. If civilization had truly died, would it be brought back to life through conquest?
Charlemagne's empire was not a rebirth of the Roman Empire in the sense of unifying the territories under Roman rule. He appropriated some Roman imagery and traditions to legitimize his rule, but he was ultimately Frankish, and governed according to Frankish custom, including dividing his empire among his sons at his death. He did, however usher in an intellectual and to some extent cultural renaissance largely through encouraging learning in monasteries, which he established and often funded, and through the improvement and construction of cities at locations like Aachen.