Roman law was used mostly because it was just better at dealing with certain issues, like contracts, debts, property inheritance, and the much less exciting background stuff, like administrative procedure in a courtroom. Probably most importantly, it was simply a complete set of laws, and Roman jurists had already done the hard work of compiling it! Medieval lawyers didn’t have to invent anything new.

First of all we should remember that Roman law was never totally “lost”. The laws were reorganized and published as the Corpus Iuris Civilis, Digest, Institutions, and Novellae under Justinian in the eastern half of the Empire in the 6th century. That post-dates the collapse of the western Empire, which was by this point ruled by Germanic kings, but parts of Italy were still ruled from Constantinople for a few centuries afterward.

But there were codifications of Roman law even before Justinian. Theodosius also issued a compilation, in 429. The Theodosian Code and other earlier collections were also used by the Germanic rulers in the former western Empire, particularly in the form of a compilation known as the Breviary of Alaric (after the Visigothic king Alaric II). The Breviary preserved Roman law in Visigothic Spain and southern France, so Roman law was used alongside Germanic law codes (issued by the Visigoths, Burgundians, Lombards, Franks, etc). The general idea was that Germanic law applied to Germanic communities and Roman law applied to Roman communities.

Eastern/Byzantine territories in Italy also still used Roman law, especially Justinian’s codes. In Constantinople, Justinian’s Latin laws were eventually expanded and translated into Greek. This kind of civil Roman law was already extremely Christianized (since all the compilations were made after the empire became Christian). Alongside Christianized civil law, there was also the canon law of the church, which sort of worked the other way around - religion influenced the civil law, but civil Roman law was also very influential on canon law.

Nevertheless there was a period in the 11th and 12th centuries where Justinian’s compilations were “rediscovered” in Italy and then by the rest of Western Europe. What that really means is they had better access to more complete versions of the texts they already knew from other sources. A legal school developed in Bologna, where scholars studied the texts and made comments (“glosses”):

“The glossators regarded Justinian’s texts as sacred and ascribed to them almost biblical authority. They accepted without question Justinian’s assurance that the texts contained no contradictions that could not be reconciled by one who tackled them with a subtle mind…and they took it for granted that the compilation as a whole contained all that was necessary to answer any conceivable legal problem.” (Stein, 46)

Germanic legal codes didn’t have this sort of authority. They were mostly concerned with settling personal disputes and preventing endless cycles of vendettas. Every member of society had a price, so if someone was assaulted or killed, they or their family could collect monetary compensation (a “wergild”). Germanic law wasn’t really rudimentary or less complex than Roman law, and it also discussed issues like marriage law, slavery, contract law, debts, property inheritance, etc. that were covered by Roman law, but the Roman codes discussed these issues in greater detail and already had a body of commentary to go along with it. Medieval glossators expanded on and improved these comments but the seeds were already there in the texts compiled by Justinian. (By the 13th century, a copy of Justinian’s Digest was not complete unless it included the “regular gloss” by the Bolognese scholar Accursius.)

Germanic customary law continued to be used alongside Roman law though, even after the Roman texts were rediscovered and spread throughout Europe. Germanic law was actually better-suited to the rural, agricultural society that had developed in northern France, England, the Holy Roman Empire - places that didn’t have a strong urban, Roman heritage. But Roman law was certainly adopted there too and both kinds of laws were used alongside each other, or even mixed together.

As I mentioned above there was also a third type of law, the canon law of the church. When Roman law was “rediscovered” in the 11th and 12th centuries, the church was inspired to create its own compilation as well. It’s no coincidence that this compilation was eventually known as the Corpus Iuris Canonici. But the initial collection in the 12th century is better known as the Decretum Gratian, after its creator Gratian.

So, it wasn’t really medieval sovereigns who made this decision, it was the legal scholars in the universities. Justinian had promised that his code was complete and every conceivable topic was covered, and medieval students of Roman law believed it. These students ended up working for the church or secular rulers, and they spread the idea of the universality of Roman law. Secular rulers could easily agree that Roman law was useful and they were happy to adopt it.

Sources:

My main source for this, and probably the best brief summary of how this all happened, is:

Peter Stein, Roman Law in European History (Cambridge University Press, 2004)