Note: I just had to stop writing. This is a poorly sourced mish-mosh of almost 30 years of researching this very topic. I'm happy to give you specific details or answers to anything I've said here, but I hope this helps to answer your question somewhat.

This is an incredibly complex question without a straight answer. Before I begin, I'm Catholic, but was raised Baptist and taught that Catholics had just incorporated a bunch of pagan gods and beliefs whole cloth into "Christianity" and wasn't really even Christian anymore. A lot of modern pagans teach the same thing. I converted to Catholicism and then ended up studying history partly because of this question, because I'd learned of the complexity of it and how much I had been misled.

OK, so, the short answer is "yes and no."

Here is, for example, a Pictish Stone from Scotland. On one hand are pre-Christian carvings depicting historical and mythological events. On the other is a cross. You must ask yourself why? Were Christians trying to overrite the Pictish past? Were converted Picts using their most precious things to artistically represent their newfound faith? Were there just not enough rocks around?

Here is an Egyptian Obelisk in the middle of St. Peter's Square in Vatican City. It was taken from Egypt (where it was, presumably, used in pagan worship) to Rome by Caligula (a pagan Roman emperor) and once dedicated to Tiberius, I think. It once stood over the circuses where Christians were martyred. Now, it says (in Latin), "Christ conquers, Christ reigns, Christ rules," and, "Christ deliver your people from all evil."

Are those pagan things that have been brought into Christianity? Sure. Are they being used in any kind of a pagan way? For the latter, at least, it kind of seems like a middle finger in the face of pagainism.

But then consider Barlaam and Josaphat, who seem clearly to have been the Buddha brought into Christianity as a saint. So much so that they were eventually removed from the Roman Catholic calendar of saints.

Then there's St. Brigit. If you skim the internet, the near universal opinion of everyone who's not Catholic (and some who are) is that Brigit was a pagan Irish goddess who was turned into a saint. And yet ... there doesn't seem to be a lot of written or archaeological evidence for this. How could there be? Druids weren't sharing their info and there wasn't a written language otherwise. Most of Irish and Norse mythology would be lost if it weren't for the Christians writing it down. There's this one part in the "Prose Edda," I think, where Odin is discovering the runes. He kills himself on Yggdrasil, the world tree, and calls it "a sacrifice of myself to myself." Sounds like Jesus, right? But then you have to remember that Snorri, who wrote it all down, was also a Christian.

Lord, look at Beowulf. A clearly pagan story about pagans, but it's equally clear that Christians wrote that story down.

What I'm trying to say is that it's so terribly difficult to parse out influence of paganism on Christianity and vice versa. Even regarding Judaism, there was a Semitic pagan thunder god named "El" and "Adonai" is cognate with "Adonis." The very word "Deity," coming from "Deus," the Latin word for God, is also cognate with Jupiter and Zeus and all of them derive from the Proto-Indo European word Dyeus Pithair (or something like that) meaning Sky Father. Hell, our word DAY is cognate with "Deus" and thus a very ancient, pagan God.

Your question about whether people just converted whole cloth and left their pagan practices behind is a great one and goes to the heart of this. We're coming up on Halloween. Did Catholics take a pagan holy day and turn it into something Christian to help convert the populace? Did they force Christianity on the populace who snuck in some of their pagan beliefs in the form of a barely Christianized holiday?

Or, and hear me out, is it just a completely natural, human and worldwide thing to do to celebrate the seasons? Is it completely normal to celebrate a birthday or the longest night of the year or the last harvest or the first planting? And maybe everybody assigns religious significance to it. And maybe some of those celebrations, whether pagan or Christian, look similar.

ABOUT ART

This is the more interesting question to me. I remember, in my Evangelical days, reading some tract about how all the depictions of Mary are continuations of depictions of a Babylonian mother goddess. But that later seemed stupid to me. Is every mother who holds her child on her lap for a photo trying to evoke some ancient goddess? Or, hear me out, is it just what mothers do?

But other questions offer more merit. Have you ever looked at the difference between Orthodox Christian and Catholic Christian (Renaissance and afterwards) art? Consider angels. In the Bible, they're wheels in wheels or a conglomeration of various beast heads or just a mishmash of wings and eyes. (I have a collection of Biblically accurate angel ornaments on my Christmas tree and I love them.) But the Roman Catholic angels began progressively more human looking and then had the introduction of those fat, baby cherubs. It seems clear that, during the Renaissance, pre-Christian artistic concepts gradually bled into Christian art and changed it considerably.

Or look at the Book of Kells. Like the Pictish Stones, you can see that what was being produced in Ireland/Scotland was veeeeeeery different than mainland art and had been highly influenced by pre-Christian artistic concepts. Also, baby Jesus has blond, curly hair.

This isn't art, per se, but consider the "Heliand," a Germanic translation of the Gospels where Jesus is a lord and his disciples are thanes and Bethlehem is a hill fort, etc.

Ethiopia is one of the most ancient Christian nations in existence and their religious art is aaaaaabsolutely gorgeous and fascinating. And clearly influenced by something completely different than Renaissance art (although shockingly similar to the Book of Kells).

As u/phantom-scribbler already noted, this is a very complex topic.

I remember having read about Charlemagne. Under his rule, a lot of monasteries were founded in what belongs to Germany now. Lots of the people who populated those monateries came from Ireland, which is one reason Carolingian Book decorations are highly influenced by a "Celtic style". But, I remember that a bishop who was located in the southern part of Germany wrote a letter, complaining about the Beltane fires still burning regularly and that the peasants would attend those pagan festivities. But unfortunately I will not be able to find any citation for this by now, I read this when I studied a couple of years ago, but it is still stuck in my head.

Next thing that comes into my mind is, that when all the Germanic tribes flowed into the Roman Empire, there in some parts already were active Christian communities, which would allow different beliefs to mingle. We have sources for a bishop in Cologne in 310, and the Franks conquered the city around fifty years later. Equally in Cologne, there is the archaeological evidence of the development of a church that once was a room in a private house, and was enlarged and rebuilt over many centuries. The church is St. Kolumba, now houses a museum, and all the older churches can be visited under the museum. During the Frankish rule in Cologne, arounf 700 AD, the private Room inside of the house gets an apse which is the archaeological evidence for a church that is thought to be older.

Another example that comes to my mind is in the South of Germany. There is a small town near Passau called Künzing. In Passau, there was also a bishop in the 5th century called Severin. He was later on a saint, and there are several stories of the wonders he could do. One story is that there was a small chapel in Künzing which had been damaged more than once by flooding of the nearby river. During another bad weather incident, Severin came over from Passau a spoke a blessing over the church, and this time the church wasn't flooded and hadn't been ever since. I cannot imagine that such a story would not have been told to new people.

Mihai Gregore did a research how the conversation of the Saxons in the 8th and 9th century worked with the adaptation of Christ into the Saxon warrior self esteem (Essay in German, 2011).

There is archaeological research dedicated to the dating of small churches built in Southwestern Germany where the Alamanni were sttling, which suggest a big amount of them comes from the sixth and seventh century. The graves that were located next to those show the classical Early Medieval burial ritual with lots of added goods - and lots of weapons. So the traditional burial style suggests paganism, but the location next to a church does not.

You have specifically asked for artwork. There is a illuminated page in a manuscript called the "Stuttgarter Psalter" which was made in the 9th century. (Kept in the Württembergische Landesbibliothek, fol. 23, digital version here: https://digital.wlb-stuttgart.de/sammlungen/sammlungsliste/werksansicht?tx_dlf%5Bdouble%5D=0&tx_dlf%5Bid%5D=8680&tx_dlf%5Border%5D=title&tx_dlf%5Bpage%5D=49&cHash=92d45e7b87ab44460faef57584fa08f9 ) Here Jesus is represented in a kind of chainmail as a warrior chieftain conquering lion and snake as symbols for evil.

I think there is an early Medieval sculpted choir barrier in France with something similar, but I have to dive into my literature and I am not quite sure if I can provide an exact citation for this...