I've been wondring about this for quite some time but couldn't find any satyisfying answers in my books or on the internet. As far as I know, most early medieval countries comprised of two major demographic elements - germanic minorites who had migrated to or conquered those lands and established their kingdoms on them and their "Roman" inhabitans who had lived there for generations. What is also known to me, is that both groups had their own laws and justice systems based on their tradition and culture. However over time those germanic people would slowly assimilate into Latin culture and adapt local customs.
And here's my question, why this assimilation didn't include adapting the Roman law?
PS: I apologize for any possible mistakes, I'm not a native english speaker
If you are talking about the northern provinces of the empire, you are completely wrong in thinking that the "barbarians" were a minority. Far from it.
But aside from that, there is one thing to be noted, which probably answers your question: people did adapt, both culturally and judicially, to Roman tradition, but when the empire "fell", that influence started to recede slowly. It wasn't a sudden transformation that deprived people of the Roman influence they acquired, it was a rather slow process, and by all accounts, incomplete, as many aspectes of Roman tradition persisted throughout the Middle Ages, partly because of the fascination that many people, and particularly the elites, felt for Classical Antiquity. This is known as "the allure of classical models".
So, Roman law did not completely disappear from Western Europe, but it did see a decline, unlike the case of the Byzantine Empire, where it was cultivated and preserved. It was precisely from Byzantium that it started to expand back into Western Europe, mostly due to the Western scholars' study of Justinian's Corpus Juris Civilis.