The late history of the Empire in the west, specifically the time frame you're referencing, gets really complicated by the fact that our main sources for these are bishops (think Gregory of Tours, for one) whose chronicles include the conversion of several of the tribes that settled in the former lands of the Empire. But to help us break this down:

1. Which of the Germanic peoples in the late 4th century / early 5th century were not Christian?
2. What records from these tribes?
3. What was the non-Christian perspective of Christianity in the Empire before its fall in the west?

The use of the word "pagan" is a bit of a catch-all used to describe polytheistic religions that existed alongside of the Abrahamic faiths, so we could be talking anything from the Germanic religions to Greco-Roman pantheons to even Zoroastrianism.

For the sake of #1, we'll be talking about Germanic faiths. The dates that the various tribes settled in the Empire differ, but we'll focus on five of the bigger confederations: the Goths (who themselves were fairly diverse), the Vandals, the Franks, the Burgundians, and the Alamanni. The first two are the most important for our story honestly, as it's these groups that bring most of the destruction of Italy and North Africa and shape the larger narrative the Romans were having about Christianity and its effects on the Empire's security. The Visigoths and Vandals had both converted to Arianism Christianity around the time that they first settled into the Empire's territories. The Franks and Burgundians were both initially "pagan" upon their settlement but converted to Nicene and Arian Christianity respectively in the following decades, both by the early 6th century. This tells us something about how they thought about Christianity: as a geopolitical tool. They couldn't have been too worried about how it changed the Empire from its "pagan" past as they watched it crumble if they themselves decided to convert, and the bigger implications of it all will actually be discussed later.

The answer for #2 is short and bittersweet: these tribes didn't leave their own documentation from before their conversion (or we haven't found them yet), and their biggest body of literature, their various law codes, come from the 6th century onwards and are largely inspired by Roman law to the point that it doesn't tell us much about their pagan beliefs.

The answer for #3 is an interesting one, not because it tells us anything about the Germanic tribes but rather the Greco-Roman intelligentsia that started the initial controversy about Christianity in the Empire. It certainly doesn't help that Edward Gibbons was an influential historian during the Enlightenment and paints the decline of the Empire in the west and basically the entire history of the Eastern Empire as "dumb dumb Christians made everything worse". This is where a lot of our own narrative of this comes in, as Gibbons obvious had more than a thousand years of hindsight to criticize what happened, but there were certainly critics back then that had their doubts about this faith. The two main ones we should talk about are Lucius of Samosata and Celsus, a Cynic and Platonic philosopher respectively who both lived in the early-mid 2nd century. Lucius is probably one of the first critics of Christianity, his big work regarding it was "The Passing of Peregrinus". It's not really a scathing critique of Christianity by modern accounts, but his satire paints Christians as gullible and delusional but also strong-willed and moral, which sets the stage for a lot of apologists. It's really Celsus that gets the ball rolling with critiquing Christianity with respect to the Empire. In "The True Doctrine" (we don't actually have the original document anymore, we just have the fragments that later Christian theologist referenced when they countered his arguments), he basically does a systematic breakdown of all of Christianity's major tenets and prophecies, calling it out at times for being unoriginal and copying from Platonic ideals, but his critique of the religion with regards to the Empire was that these communities would never be completely loyal to the Emperor because they would never worship the Emperor to the same extent as God. This is a pretty rough overview of the work (I would definitely recommend checking out Origen of Alexandria's thorough responses to Celsus), but this is the initial precedent of doubt of Christianity in the Empire. The culmination of these doubts came as the Visigoths sacked Rome in 410, coming mostly from the senatorial class and aristocracy of the city rather than the common person, and its from this event that we get one of the more iconic works of Christianity theology in late Antiquity: Saint Augustine's work "The City of God". Without getting too much into the weeds about the details, this work synthesizes a lot of previous theologian thought about the role the Empire had in Christianity, basically transforming Rome into the "New Jerusalem". It was the most holy of governments, ordained by God himself, and its fall was believed to trigger the end times as predicted in the Book of Revelations, merging the idea of Rome with "New Babylon". "The City of God" is honestly one of the most influential works that really cemented the idea of an obligatory union between Church and State that affects politics even up till today to some extent. More importantly, it also ties back in to the Germanic tribes and their usage of Christianity as not only a way to assimilate with their new subjects but also as a tool of political legitimacy.

So yeah, that was a huge paragraph, but here's a TL;DR:

1. A lot of the destruction of the Empire in the west in the 4th and 5th centuries was done by Germanic tribes that had already converted to Christianity in one form or another or from tribes that could convert not long after they migrated. We haven't found any records from their polytheistic past in which they talk about Rome and its fall from glory.
2. There certainly was criticism about Christianity and its effects on the Empire's unity, but a lot of this was confined to Greco-Roman philosophers and Rome's aristocracy, especially after the Sack of Rome. However, Christian theologists had been discussing that political aspect for a while by that point. "The City of God" is a great work to show that, by the mid 5th century, Christianity had intertwined with the state so much that the decline of the Empire was deemed either literally impossible (because God has ordained the Emperor and the state as a whole) or ultimately good (because of the apocalypse and whatnot).