One of the goals of Charlemagne, who was crowned as Emperor of the Romans by Pope Leo III on Christmas Day, 800, was to revive the glory and unity of the Roman Empire in Western Europe. His empire was therefore closely associated with the Roman heritage, in terms of culture, administration, religion, and even imperial symbols like the eagle. Charlemagne promoted the codification of laws and standardization of religious practices based on ancient Roman models.
So, while the Carolingian Empire was not literally a continuation of the Roman Empire, it self-consciously positioned itself as a revived Roman imperial polity in Western Europe, making several connections and drawing inspirations from its ancient predecessor. Charlemagne aimed to rekindle not only Roman political achievements but also the values and culture associated with the old western Roman Empire.