Rome never really "fell" as historians have claimed for several centuries; it did evolve into something quite different than what it had started in antiquity, from a loose alliance, to a republic, to an empire, and finally to just a cultural force. Of course, the Empire collapsed, but the influence of Rome was felt for centuries long after the traditional date of 476 when the Western Empire became more and more politically and economically impotent.
Charlemagne (742-814) ruled quite a bit later than the Empire; he was, however, a strong enough ruler to keep most of the former Western Empire cohesive, at least for a few generations after him. Was he a "Roman Emperor?" Only in name, but he did use the cultural artifacts of Rome to keep his portion of the former Empire intact. Ironically, the concept of "Roman Emperor" continued for a millennia, until Napoleon finally did away with the "Holy Roman Empire" and its office of "Emperor" in 1804! See the link for an interesting list: