How did charlemagne's relationship with the catholic church benefit both parties

Charlamagne and the Roman Catholic Church were on good terms with each other.  He fought and defeated other groups and converted them to Christianity.  That relationship was further strengthen when Pope Leo III fled from Rome in 799 A.D. and asked for his help to restore him.  On Christmas Day, he crowned “Emperor of the Romans” by the pope.  This made him the first Emperor of Western Europe and with the support of the Church, his rule flourished. He also  strengthened the spiritual power of the Church and in turn gained the support of the clergy.