The late 12th century to the early 13th century Iceland can be regarded as a second golden age of the skaldic poems with full of kennings on ‘pagan’ representations. They became a kind of medieval ‘cultural heritage’, inherited from the pagan Viking Age, but were no longer regarded as a living threat against the Christianity, just as the Greek and Roman deities were in Medieval West. Guðrún Nordal even argues that the poems and the knowledge of pagan lore (kennings) now constituted an indispensable tools in learnings and education in contemporary Iceland for the elites to distinguish themselves politically as well as culturally (Guðrún Nordal 2001). In other words, the 12th and 13th century Icelandic elites like Snorri SturlusonSturulson competed each other to monopolize and to make use of cultural resources like skaldic poems to strengthen their position in Icelandic society.

 

Then, why they were struggling so hard? The contemporary power struggle among the Icelandic chieftains and the concentration of power offers its answer: It culminated in the final phase of Icelandic Commonwealth period, known as the Age of the Sturlungs. In order to survival this political turmoil, some Icelandic elites sought the help from outside, i.e. the king of Norway. Though still also in the severe political disturbance called ‘Civil War Period (1130-1240), the political alliance between young King Håkon IV of Norway (r. 1217-1263) and Jarl Skuli (d. 1240) secured a temporal truce ([edited 2]:) in Norway, and their political influence must have been very attractive in the eye of the Icelanders. Snorri was no exception – he rather paid much attention to such contemporary political development in Norway. According to the Catalogue of Skaldic Poets, Skáldatal, Snorri was said to dedicate his own skaldic poems to five Norwegian rulers, including King Håkon and Skuli. The art of skaldic poem was one of few salespoint for the Icelandic elites to impress Scandinavian rulers: While the names of several Scandinavian rulers were recorded in this catalogue, a recent study suggests that they may also had indigenous (i.e. Norwegian) skalds in their court. It means that Snorri had to compete not only with his fellow Icelanders, but also with Norwegian rival poets to sell himself as superior to the potential patron. Thus, Snorri’s politics and literary activity were heavily entwined in his life, also leading to his final downfall in 1241 (He made a mistake of supporting the loser side of the finale of Norwegian Civil War, Skuli against King Håkon).

 

Reference:

• Guðrún Nordal. Tools of Literacy: The Role of Skaldic Verse in Icelandic Textual Culture of the Twelfth and Thirteenth Centuries. Toronto: U of Toronto P, 2001.

• Wanner, Kevin J. Snorri Sturluson and the Edda: The Conversion of Cultural Capital in Medieval Scandinavia. Toronto: U of Toronto P, 2008.

• [Edited]: typo fixes.

• [Edited 2]: typo fixes of the name of the source/ complemend the title of the person mentioned (sorry)

I wrote quite a bit about this in this thread - but in short one main motive of Snorri was to preserve and promote the old legacy of Skaldic poetry. Teaching young poets is also a stated motive (Uppsala Edda ch 34); where Snorri interrupts a dialog between Ægir and Bragi to apparently state the purpose of his work:

But this must be said to young poets that desire to learn the language of poetry and furnish themelves with a wide vocabulary using traditional terms or understand what is composed obscurely, then let him take this book as entertainment. But these narratives are not to be consigned to oblivion or demonstrated to be false, nor are ancient kennings that major poets have been happy to use to be removed from the poetry. Yet Christian people are not to believe or be convinced that it has been thus. [Faulkes' translation]

But this is not to say there are not other motives, although there is no certain answer exactly what they are (but many opinions)

In Snorri's day, by the year 1200, Iceland is thoroughly christian, have officially converted in the year 1000 and already gone through a period of puritanism in the the mid-late 11th century where (among other things) the Icelanders renamed the days of the week; the only Scandinavians to do so. By 1200 it was not a serious threat in Iceland (whereas in the Uppland region of Sweden, it may have been within living memory at the time). The fact that Snorri regarded the Norse gods as equivalent to the Greek-Roman ones is explicit as you've seen.

By 1200 Iceland has two bishops (Skáholt and Hólar) and two Benedictine monasteries (Þingeyraklaustur and Munkaþverá). This means more educated monks and clergy per-capita than anywhere else in Scandinavia, and its in this that one might find the roots of Iceland's strong literary culture. It also helps that Iceland was relatively peaceful at the time, while Norway and to a lesser extent (or less documented extent) Sweden were embroiled in civil war as fluid constellations of kings and nobles (extending across Scandinavian borders) vied for power.

Arguably the intellectual center of all Europe in that time, and certainly for Scandianvians, was Paris and the surrounding region (Reims, Soissons, Sens). Much of high medieval culture was coming into being there; the chanson de geste, the Roman de Troie and more generally the "Matter of Troy" and "Matter of Rome" categories of stories (as well as the categorization). You had significant intellectual figures like Bernard of Clairvaux, founder of the Cistercian order, Abbot Suger of Saint-Denis who largely created Gothic architecture, the immensely popular teacher Peter Abelard. Students from all over Europe were flocking there, not just Scandinavia. But to mention some; From Iceland there was for instance Bishop-Saint Þorlákr, a somewhat contemporary to Snorri who studied there. The first archbishop of Sweden was anointed there, in Sens cathedral in 1164 by Danish archbishop Eskil, who had studied there extensively and befriended Bernard, who in turn sent his followers to found monasteries in Scandinavia (Herrevad, Alvastra, Varnhem, Julita, etc). Eskil's successor the famous Absalon studied in Paris as well, and so forth. Snorri himself was not educated abroad, but he certainly knew those who were.

Later in history there were more English and German contacts and influences but in the century around 1200 it is first to France that one should look to find the source of foreign influences in Scandinavia. I could easily give a dozen concrete examples of such influnces but in the name of breviety the one we're interested in here is whether there's reason to think Snorri may have been influenced from there to invent this sort of Aeneid-ish origin story for the Icelanders (and really all Germanic peoples). And there is plenty of such reason.

As mentioned the epic poem the Romane de Troie was a big hit in literature in the late 12th century France. Another version of the Matter of Troy was translated into Icelandic not long after the Eddas as Trójumanna Saga, but was based not on the Romane de Troie but more on the older story by Dares Phrygius. (but not directly; which version of the story the Trójumanna Saga is based on is unknown as far as I know, and possibly lost) Another chronicle based on Phrygius' account, written in north France approximately the same time as Snorri was writing his Edda, is the Histoire ancienne jusqu'à César (Ancient history until Ceasar). This is another Aeneid-ish story (the Aenied being Virgil's poem that describes the mythical founding of Rome as coming from Troy) which derives the ancestry of the French kings from Troy, but also includes other bits of Greek mythology that cover some of the same ground as the prologue to Snorri's Edda (the long version in the Codex Wormianus).

There is an older possible source of inspiration from France though; Dudo of Saint-Quentin wrote the History of the Normans in the early 11th century and he (also acquainted with the Aeneid), put the origins of the Danes in Troy. It's not obvious that Snorri knew of him, but the Danish chronicler Saxo Grammaticus did, although he has an entirely origin different story for the Scandinavians/Germanics. Like Snorri he does engage in euhemerism, but the details are different; Odin supposedly resided in Uppsala rather than Old Sigtuna. This is not a problem with Christianity at all; on the contrary both of them are creating stories which explain the origins of these false gods while simultaneously denying their divinity. While there were, to varying extents, attempts at eradicating anything perceived as a remnant pagan cult, there was by and large no attempt to pretend or reason to pretend that paganism hadn't existed.

150 years or so earlier, in the late 11th century it was a bit different; The Bishop's Sagas tells of Icelandic Bishop Jón Ögmundsson (who also may have studied in Paris). It's him who pushed for the renaming of weekdays, but he was acting within living memory of paganism (his own memory, even) Perhaps because of that he had a puritanical streak which went well beyond most Christians of his day; having viewed dancing and singing as un-Christian as well.

In any case; Snorri's prologue is likely to be his own contemporary composition and not representing a Scandinavian tradition; as it is very much in-step with the continental literature and historiography that were popular at that time. But with all this foreign influence, with these chansons and other continental literature coming to Iceland, Snorri obviously wants to preserve and promote the older traditions. Skáldskaparmál is the main book here, the guide to writing poetry, while the poetic Edda contains much of what he knew of the skaldic poetry itself. Gylfaginning contains fragments of older skaldic poetry but also Snorri's interpretations and elaborations on them. Which is not at all to say the prose parts are all Snorri's invention - e.g. Thor's legs going through the boat (Gylfaginning 48) is not in the Poetic Edda version (Hymiskviða) but visible on for instance the Altuna Runestone (U1161).

Although some Christian religious influences likely found their way in, Snorri's point is not to reconcile the mythology of his forefathers with Christianity. Snorri's euhemerism is clearly at odds with the rest of the Edda (outside his notes) and the Poetic Edda. In his view his forefathers believed was mistaken, and what the prologue tells you is how he thinks that mistake came about, while also explaining the lineage of Scandinavian dynasties back to Genesis, explaining how they fit into the classical world as well as the King's Sagas he himself and others recorded, and even giving a theory of the Germanic languages. He is seeking to raise the status of their culture and history by integrating it into that of the western Christian world (including he classical world); and in that sense there is plenty of Christian influence. Much as for instance the 13th century Gesta Hungarorum traced the Hungarians back and invented their relationship to the Huns, thus giving them a place in the classical world. Or, as in Sweden, derive a Gothic ancestry.

Snorri's patriotism is hardly selfless though. He includes his family (the Sturlungs) at the end of this great geneaology, making himself thus an ancestor of not just the 'real' Odin, Thor and Freyr but also of king Priam of Troy and the 'real' Saturn and Jupiter. It should also be seen in light of the Norwegian kings claiming sovereignity over Iceland and the Sturlung's role in the domestic conflict which began around the time the Eddas were finished. Personal, literary, familial and political motives abound.

But as I wrote earlier, but it bears repreating that the skaldic poetry was poetry, not scripture nor liturgy. It was written as entertainment, to be performed by skalds at banquets and such for the jarls and kings and powerful people. Although they are very important sources that reveal a great deal about a great deal of things, they do not say much about the practical worship and cult that existed. Nor does the prose sources that Snorri must have had (e.g. with Thor's fishing, but also things's like Thor's journey to Útgarða-Loki, which has no poem but is alluded to in old poems and must thus have been a common tale)