There was no such event as "the Europeanization". Viking Age Scandinavia was European. The region of Scandinavia and North Germany had been in close contact with the rest of continental Europe since the first century BC heralded the start of the Roman Iron Age in that region. Contacts and influences never stopped after that. So there was a thousand years of continental contacts by the time of the Viking Age. Just because they weren't Christian yet didn't mean they didn't have outside influences, and once they became Christian it didn't mean they lost their own culture and becaeme some sort of 'generic European'. (Even as much as Viking Romantics seem to want to pretend otherwise)

Certainly there were new influences when Christianity was introduced, but the same goes for the centuries preceding the end of the Viking Age as well. In short it's not history but a Romantic cliché that there was some static and 'pure' Germanic culture in Scandinavia that completely lost its distinctiveness at the end of the Viking Age.

Now, if by longboats you mean proper longships then there was little need for that construction by the end of the Viking Age. Longships were fast-sailing warships not built for naval warfare but raids on land where their shallow keels allowed them to easily get onto and off shores and up rivers. As raiding petered out, demand for longships specifically did as well. (largely) They could not carry much cargo at all, not least in relation to the crew size.

When it comes to hauling cargo the Viking Age ship type was the knarr. Those continued to be used after the Viking Age but were eventually out-competed by the Hanseatic cog in the Middle Ages, which could carry more cargo and were better defended against raiders at sea, with their raised fore and aft decks. The Knarr simply didn't have many advantages. The cog is not some 'European' design distinct from Viking Age ones though; it is a clinker-built ship just like the Viking Age ships were (and unlike the carvel-built ships of the Mediterranean); it's still a distinctly Baltic Sea design.

If by 'longboats' you mean any boat built using the technique then those weren't abandoned at all. The snekke/snipa continued to develop and be used, as well as subtypes like the fembøring and kyrkbåt. Older ship types persisted until present day, where it made sense to use them.