Constantine didn't have any role in the Biblical Canon. The only contribution Constantine made was that he ordered 50 copies of the Scriptures to be made to be placed in the new 50 churches which he had built. He had nothing to do with what the contents of those Bibles contained. Also, looking at our oldest Biblical codices which date to this time, there's a very good chance that Codex Sinaiticus may be an example of what these Bibles looked like. Codex Sinaiticus shows us a New Testament Canon still in flux; as it does not contain books like the Revelation of John, but did contain the Epistle of Clement and the Shepherd of Hermas. So far from Constantine "freezing" anything, it may be thanks to intensified and more organized efforts to copy the Scriptures that we actually have a better snapshot of what the evolution of the Canon looked like in Late Antiquity.
Also, Constantine converted to Christianity; though his actual commitment to his new religion is up for debate. But saying he was "pagan emperor Constantine" makes an assumption about Constantine that is unjustified--perhaps Constantine did still cling to some of his pagan past, but he also seemed quite intent on showing favoritism to his new adopted religion. That's why he sponsored church building projects, it's why he personally oversaw the gathering of bishops at Nicea to address the Arian controversy.
Constantine is a complicated historical figure. And I have generally found that he is a very misunderstood figure. There are both those who want to demonize Constantine and those who want to beatify Constantine. The truth is more nuanced and arguably much less sensational: Constantine was a schrewd politician who wanted to secure and strengthen the Roman Empire. To that end his ambition led him to overthrow Maxentius in the West, and later Licinius in the East. He moved the seat of imperial power from Rome to Byzantium (renaming it Constantinople) in order to be closer to the long-time rivals of Rome, the Persian Empire (the Sassanians having filled in the vacuum of the older Parthians). Constantine legalized Christianity, and gave equal rights to Christian clergy. He also seemed to be concerned about the emerging tension in the eastern parts of the empire where the Arian controversy was erupting. Constantine was likely motivated more by desiring civil peace rather than actual theology--as he was very unlikely to have fully understood the the complicated theological issues being debated.
To speak to the latter, concerning Constnatine unlikely to have understood the theological debates of the time; not long after the Council of Nicea (which Constantine himself had personally asked the bishops to gather for), and even though the Council of Nicea declared Arius' position explicitly heretical, Constantine was convinced by several of his religious acquaintances (in particular Eusebius of Nicomedia, himself an Arian) that Arius actually didn't disagree with the Council or the Creed it produced. As a result Constantine had the rightful bishop of Alexandria (Athanasius, remembered as St. Athanasius the Great, Defender of the Faith) exiled and had Arius installed as bishop.
Indeed, when Constantine finally received Christian Baptism on his deathbed, it was from his friend Eusebius of Nicomedia (who was, as noted, an Arian, a heretic). After Constantine's death his two surviving sons were divided: Constantinius, the elder son was a devout Arian, while Constans, the younger son, was a devout confessor of the Nicene Creed. However Constantinius would eventually secure power. Most of Constantine's successors were Arians. It wouldn't be until after the death of Julian, the last of the Constantinian Dynasty, who though having been raised as an Arian came to reject the Christian religion in favor of a modified Paganism. After Julian's sudden and unexpected death, the Constantinian Dynasty ended.
Was Constantine himself a devout Christian? Again, it's unclear. Though it is telling that he chose Christian clergy to be the educators for his sons, and that even though he waited until his death bed, he did ultimately get baptized (and although he asked a heretic to perform it, it was nevertheless a valid Christian Baptism). So if nothing else, even if Constantine hadn't been a "true believer" earlier in his life, the moment he received Holy Baptism he absolutely was a Christian.
-CryptoLutheran
