The medieval church was a unifying force in europe after the fall of rome because it offered -

Stability and security.

Explanation:

Theodosius first made Christianity the state religion of the Roman Empire and in 380 A. D. In the next century, the Roman empire fell and there was no single ruler to control and stabilize Europe. The power vacuum gave Christian Church an environment to expand its domain. It brought the diversity of Europe under one umbrella. The Pope became the head of Western Europe and the next level of hierarchy was in the hands of the local Church.