What is the name of Charlemagne's capital city?

Charlemagne's capital city was Aachen, in modern-day western Germany.

Aachen became Charlemagne's principal residence and the political center of the Carolingian Empire during the 790s. Before this change, Frankish rulers maintained an itinerant court, moving among royal estates. Aachen offered strategic advantages: it lay near the eastern frontier, close to the Saxon lands Charlemagne was fighting to control, and it stood in the Austrasian heartland associated with his family.

Charlemagne also valued Aachen's hot springs, which had attracted Roman settlement centuries earlier. He developed a monumental palace complex there, designed by Odo of Metz, including the Palatine Chapel. The chapel, now part of Aachen Cathedral, became the emperor's ceremonial church and burial place after his death in 814.

The question sometimes causes confusion because Paris had been the capital of the Frankish kingdom under earlier rulers, while Rome remained the symbolic center of the papacy and ancient empire. Aachen was not a capital in exactly the modern bureaucratic sense, but it was the fixed seat of Charlemagne's court and government. Later German kings and emperors continued to associate Aachen with his imperial legacy.