Final answer:
Charlemagne significantly influenced Western Europe by expanding his empire's territory, promoting the intertwining of political and religious authority, and initiating cultural and educational reforms known as the Carolingian Renaissance. Option c is the most accurate in describing his impact.
Step-by-step explanation:
Charlemagne significantly shaped Western Europe through a variety of actions and reforms. Through his conquests, he expanded the territory of his empire, laying the foundation for what became known as the Holy Roman Empire. However, Charlemagne did not begin the Crusades; therefore, option d is incorrect. Moreover, while he did promote feudalism in a general sense, the formal and structured system as we understand it today was not developed during his reign, making option a incorrect as well. Furthermore, option b is misleading because Charlemagne did not invade the Holy Roman Empire; instead, he expanded the territories under his control, which later got associated with the Holy Roman Empire.
Charlemagne united Western Europe largely through his military conquests and alliances, as well as through his coronation by Pope Leo III, which affirmed his legitimacy and authority. This would suggest that option c is accurate - he did reunite the region under his rule, especially as the first emperor to do so since the classical Roman era. His efforts included reorganizing the Church and promoting a revival of education and literacy, known historically as the Carolingian Renaissance.
His sponsorship of arts and education, his religious reforms, and his diplomatic relations with various rulers, including Muslim leaders, also showcase his impact on the culture and society of Western Europe beyond mere territorial changes. Though Charlemagne's successors could not maintain the unity of his empire, his reign set a precedent for centralized rule, cultural flowering, and the intertwining of religious and political authority in medieval Europe.