This is a good question. Charlemagne was a pivotal figure in the ancient world. He lived from 742-814 and was king of the Franks from 768 and was then Emperor of the Romans from 800-814 (He was crowned as such by Pope Leo III on the symbolic day of December 25th 800).
In terms of whether he was a Roman, it all depends on what you mean by Roman. If you mean a traditional Roman from the days of the Augustus, then he was only partially Roman, because Christianity, for instance, became central to the reign of Charlemagne. He even persecuted anything that resembled paganism. If we define being Roman in terms of someone like Constantine, then he was much closer, but there were still some important differences. For instance, he allowed the catholic church to crown him, which was a new development.
In light of all these points, it is best to say that he was partially Roman. By this time, there was so much transformation that had taken place in the Roman west that Charlemagne worked with what he had. Moreover, there was still a Roman East that claimed direct connection with the Roman past.