Final answer:
Charlemagne significantly influenced European political and spiritual domains by establishing the Holy Roman Empire and promoting Christian values. Pope Gregory the Great solidified the papacy's power, expanded Christianity, and gave shape to the church's influence during the early Middle Ages.
Step-by-step explanation:
From the first list, Charlemagne was a key figure in the early European Middle Ages, creating a vast empire that brought together disparate territories, laying the groundwork for future political structures, and advancing the Christianization of Europe. His coronation as Emperor in 800 by Pope Leo III signaled a new era in European history with the establishment of the Holy Roman Empire, affecting the cultural and political dynamics of the continent. Charlemagne's reign saw significant military conquests, efforts to revive learning, and close ties with the papacy, reinforcing the influence of Christian values in governance.
From the second list, Pope Gregory the Great played a crucial role in asserting the independence of the papacy during a time when Rome was under threat and lacked Byzantine protection. By skillfully managing alliances with various Germanic kings and expanding Christianity into Germanic territories, Gregory established the papal authority that would shape the Christian tradition in Europe and influence medieval political dynamics.