what were the boundaries of Charlemagne's empire?

Charlemagne's empire, also known as the Carolingian Empire, reached its height in the late 8th and early 9th centuries, encompassing much of Western and Central Europe. Its boundaries included present-day France, Germany, the Low Countries, Switzerland, Austria, and parts of Italy and Spain. The empire was established through conquests and alliances, and its borders fluctuated due to military campaigns and treaties. Charlemagne's rule laid the foundation for later European states and the Holy Roman Empire.