Final answer:
The alliance with the popes, the Latin Church, and the feudal system held European society together after the fall of the Carolingian Empire.
Step-by-step explanation:
After the fall of the Carolingian Empire, several factors held European society together. One significant factor was the alliance between the Carolingian rulers and the popes, which allowed them to work independently from the Byzantine Empire and establish their own territories.
The Latin Church also played a crucial role in uniting Western Europe and providing a sense of European identity. Additionally, the feudal system emerged as a social structure that provided security and created relationships of loyalty and service between lords and vassals.