The Roman emperors just acted like Roman emperors. That's how things were done back then, you are blaming the religion for the actions of the Roman state. When Christianity became the official religion of the empire, it occupied the same place paganism did before, but strangely enough, nobody ever accuses paganism of having been spread through "violence" or "persecution". That charge is only leveled at Christianity for some strange reason. When Julian the Apostate came into power, he engaged in widespread persecution and discrimination against Christians in his effort to restore paganism, but somehow his actions do not reflect negatively on paganism like those of Christian emperors do when it comes to Christianity.
Of course, in neither case was the persecution and violence as widespread as the nu-atheists would have you believe, but that's neither here nor there. None of this is proof that Christianity was spread solely and purely through violence. For more than three centuries, Christianity was actually a persecuted sect and the subject of systematic suppression by the Roman state (which again does not seem to reflect negatively on paganism for some odd reason). Somehow, it still managed to thrive and expand, despite the fact Christians were in no position to impose their religion on anyone by force. The nu-atheists of course provide no explanation for the spread of Christianity throughout the empire prior to it becoming the official religion of the Roman state.
Much like they have no explanation for the conversion of the barbarians after the collapse of the western Roman empire, where the Church was in no position to impose anything on anyone, least of all through violence. Nu-atheists will just generally name drop Charlemagne, like you just did, in hope people will ignore every other case in which the barbarians converted on their own free will, starting with the Franks themselves, and ending with the Normans, who converted after putting the Franks through the sword and not the other way around.
They'll also ignore the actual motives for Charlemagne's supposed "forced" conversion of the Saxons through slaughter, which was not actually a forced conversion at all (forced conversions were forbidden by the Church, and if Charlemagne had done anything his accusers say he had done, he would have been deemed an heretic), and had nothing to do with Christianity at all. Charlemagne slaughtered the Saxon rebels in frustration because they rebelled constantly and were a continuous thorn at the side of the Carolingian Empire at a time when Charlemagne was engaged in serious military campaigns on two fronts, against the Moors and the Lombards respectively. That's the reality.
This warrants some further explanation, so let's look at the history of this event in detail. His first campaign against the Saxons began because the Saxons attacked the Carolingian Empire and sacked several cities and churches along its frontier. Charlemagne had to personally intervene, and after putting them down the first time, destroying their shrine Irminsul in revenge for the Saxons destroying and ravaging churches across the border of the empire, the Saxons attacked Hesse and destroyed any church there while Charlemagne was away in Italy campaigning against the Lombards. Charlemagne was forced to turn his attention away from his engagement with the Lombards, and met the Saxons in battle in 775. After defeating them a second time, the Saxons gave hostages and swore oaths of loyalty to the Frankish Empire. But when Charlemagne returned to his campaign against the Lombards in 776, the Saxons rebelled again, violating their oath of fealty. Charlemagne once again left Italy, and you can imagine his state of mind at this point, and crossed the Alps to defeat them in Saxony for the third time. In order to avoid punishment for their treachery, the Saxons swore to become Christians and recognize the authority of Charlemagne and the Franks. As a promise of their subjugation they pledged their fatherland to Charlemagne. They essentially became subjects of the Carolingian Empire, and Saxony now belonged to the Empire. The royal annals state that if the Saxons failed to keep their oaths of loyalty, they would become traitors of the Empire, and treason was an act punishable by death.
To cement their subjection, Charlemagne established a stronghold in Saxony known as Karlsburg. Believing that the Saxons were finally pacified, Charlemagne left yet again to campaign against the Moors in Spain. The Saxons, in their infinite wisdom, took advantage of Charlemagne's absence and went on a rampage, destroying Karlsburg, sacking churches, plundering all their way along the Rhine up to Koblenz. This act infuriated Charlemagne to no end, least of all because he was forced to pull away from his campaign against the Moors. He met the Saxons a fourth time, and the Saxons again surrendered unconditionally. Thinking he had finally subjugated them for good, Charlemagne even appointed several Saxon nobles as counts in 782.
Now get this. Not long after that the Slavs began attacking the Saxons and Thuringians in the East. Given that the Saxons were nowt subjects of the Empire, Charlemagne actually sent a mixed Frankish-Saxon force to deal with the Slavs, essentially taking action to defend the Saxons against an invader. Of course, the Saxons, being the treacherous scumbags that they were, rebelled yet again, and with the help of the Slavs slaughtered the Frankish army Charlemagne had sent to defend the Saxons in the first damn place. Charlemagne's own marshal and chamberlain were killed as well. Now this was high treason, and when Charlemagne squashed the Saxons for a fifth time, this time he was dealing with an act of treason of the first order, and it is at this point that he slaughtered "over 5000 Saxons", as we are told by the nu-atheists (the figure given by the annals is actually 4.500, and there's reason to believe this number was inflated, as was often the case in those days). Those 5000 Saxons were killed not because they were "pagan", but because they were traitors. It was after this that Charlemagne issued the Capitulatio de partibus Saxonie which prescribed the death penalty for refusing baptism, destroying churches, violating the loyalty oath, and plotting against Christians, all things the Saxons did over and over, spitting in the face of Charlemagne's considerable magnanimity up to that point, especially given the standards of that of time. The edict also mentions the death penalty also applied to cannibalism and human sacrifice which must have still been practiced by the Saxons, but you never hear about that by the nu-atheists.
And that's the history of the supposed "forced" conversion of the Saxons by the "fanatic" Charlemagne, the guy whose greatness as a king went so far as impressing Harun al-Rashid, himself a great monarch, who established a cordial relationship with the Franks and sent Charlemagne many presents as recognition of this friendship.
Now, i'm not gonna say that every case of violence instigated by a Christian monarch or a Pope must invariably have had some kind of similar justification, but to the degree that violence erupted from the bosom of Christendom it did so owning to human failure and not to anything pertaining to the Christian faith. Furthermore, to focus on such instances while ignoring everything else Christianity has produced is the most puerile form of sophistry. Do you not think the writings of the fathers of the Church had any role in the conversion and spreading of the faith? Do you not suppose that anyone might have been converted after listening to a sermon, or by being impressed by the examples of the saints? Christianity produced a vast body of literary works, and most of those writings were devoted to the justification of the faith, either according to theological but also, as you yourself pointed out, philosophical arguments. A Clement of Alexandria, a St. Augustine, a St. Thomas Aquinas, a Gregory of Palamas, none of those people apparently had any role in spreading the Christian religion. The adoption of this religion by so many disparaging cultures and peoples occurred through the sword only. No other means were ever employed. No argument was ever issued forth by a Christian intellectual. No preaching by a Christian theologian or saint. Never, only violence, or fear mongering. Or so we are told by those who, coincidentally i'm sure, have a vested interest in discrediting the Christian faith.