The Franks were the most important barbarian group in because they were Catholic. All of the other barbarian groups such as the Visigoths and Vandals converted to the Arian heresy. This heresy teaches that Jesus was subordinate to God the father. This meant that the Catholic church and pope did not trust the Arian rulers and therefore the native Romans and barbarian Arians did not trust each other. But by the 8th century most barbarians had been converted to Catholicism. But the Franks converted directly to Catholicism which made the pope trust the Franks more. The way a people would be converted in this time was that the king would convert and then the people would follow. Rome was facing threats from the Lombard barbarians that lived to the south and north of Rome. The Byzantine empire was the traditional protector of the pope but they were often off fighting the Persians and the pope was subject to the whims of the emperor. Pope Martin had been banished by Constans the second and pope Severinus had not been recognized as pope by the Byzantine emperor because he refused to accept Monothelitism. But in the 8th century The Frankish king Charlemagne became the official protector of the pope. After Charlemagne had defeated the Lombards he gave them as a gift to the pope which became the papal states. The Vatican city is still a papal state today.
The Franks had been ruled by an old prestigious family called the Merovingians for a long time. The most well known Merovingian king is probably King Clovis. But as time went on more and more Merovingian kings ended up being children or having mental defects. The power over time ended up all going to the mayor of the palace which is similar to a prime minister. By the time Pepin was Mayor of the Palace the king had no power at all and just had the title. Pepin wanted to displace the king so that he could become ruler. But if he did that the Franks would consider him illegitimate. So Pepin appealed to the pope to dispose of the old king and to make him become ruler. The pope agreed so the Merovingian king was sent to a monastery and Pepin became king. This was the beginning of the Frankish Carolingian dynasty.