Well, you see, Charlemagne was a pragmatic man. He decided to invade Saxony for two reasons.

• More lands!
• More importantly, the Saxons were constantly raiding and pillaging his kingdom and as a Frank king, he had the obligation to retaliate or appear weak (I kid you not). Therefore, he decided to enter Saxony with his army, multiple times to submit them. They said that they would convert but always decided to revert back to their old religion and as you might know, after a certain time he decided to put really harsh measures on the Saxons so they would stop being pagans. For example, any case of idolatry would be punished by death, or if you were caught lighting a candle in a special place known for being pagan then you had to pay a (huge) fine.

Why did he convert them? Well, you said that it helped pacify them and this is true, but there is also the fact that Charlemagne was a really smart man that decided to link the fact that the Frankish subjects had to have a common thing between each other and for him it was religion. He never really cared about changing their cultures, their ways etc, but if you were part of the Frankish Kingdom you HAD to be Christian, it was part of the common identity of being a Frankish subject.

For example, you could be Saxon, living like a Saxon but practising Christianity, and I could be a Briton, and the only things that would ‘link’ us would be the fact that we are Christian and we are both subjects to the same King.

tl; dr: He converted everyone in his kingdom to create a common identity.

Something really important to understand as well, Charlemagne never really cared about spreading Catholicism outside of his realm, when the Franks raided the Avars but did not conquer a significant part of their territory they never really cared about converting this foreign kingdom to Catholicism. It is only if you were a subject of Charlemagne that you had no choice but to BE Catholic.

Source (in French): Charlemagne – Georges Minois (2014)

A significant part of it was just a history of conflict between the Franks and the pagans of that region. Warfare for Germanic tribes was focused on raiding and pirating, usually sacking border villages and temples in small bands (~100 men) for the purpose of accumulating wealth and prestige rather than land. They typically weren't centralized enough to unite under a single banner and wage pitched battles, which is why Rome dominated them until its downfall.

The fall of Rome led to a power vaccuum that the Franks filled under the Merovingian dynasty, which would hold power for three centuries until Charlemagne's Carolingian dynasty. The Merovingians were converted to Christianity, which made them fairly unique among their neighbors. This difference in religion and culture only provoked conflict, which tended to result in the expansion of Frankish borders.

The Germanic tribes further away from Rome's influence stuck more to the old ways, largely remaining tribal, egalitarian, and pagan. Their governments were still decentralized, and as such their warfare still focused on raiding. The comparatively rich and culturally different Franks with their lavish Christian temples were obviously prime targets.

These tendencies caused tension along borders, and in fact the burning of a church was the justification for Charlemagne's first war with the Saxons. This wasn't new to the Franks, though. Before the Saxons were the Frisians, and before the Frisians were the Suebi/Alemanni. At this point it had become tradition to conquer the pagans and forcefully convert them, pacifying their enemies and protecting their people.