Final answer:
The fall of Charlemagne's empire led to political fragmentation and the development of feudalism in Western Europe, and it increased the influence and stabilizing role of the Catholic Church across the region.
Step-by-step explanation:
The event that was caused by Charlemagne's empire falling to other invading Germanic tribes in Western Europe was the development of feudalism. After the dissolution of Charlemagne's strong government, Western Europe experienced significant political fragmentation. This fragmentation led to a system where political and military power was dispersed among local lords who ruled over their own lands and offered protection to the peasants living on them in return for services and labor, a system that is the hallmark of feudal society.
Furthermore, the rise of the Catholic Church as a stabilizing force can also be attributed to this period. The Church provided a unifying Christian identity across Europe and helped to legitimize new rulers. Monasteries and bishops played key roles in education and administration amidst the political disarray following the empire's collapse.