It's something of a misnomer to speak of Medieval Europe as somehow benighted, and the so-called "Dark Ages" were only dark in comparison with the Roman Empire that preceded them. They were, in fact, still spreading knowledge and educating students, and in more subjects than simply Aristotle and Canon law.
As early as the 11th century-- before the end of the Viking Age-- what we now call Universities were being founded in places such as Bologna and Oxford. By the 15th century nearly 90 universities were in operation across Europe, and each was open to students from across Europe and was known as a studium generale (differentiated from the studium particulare, which only catered to local students). To put this into an RPG perspective, that would put a university in roughly all of the named towns and cities on the World of Greyhawk map, and some of the largest cities would sport several.
The curriculum in those early universities, and the nature of the universities themselves, varied. Some, such as the great studium in Genoa, was organized by, and under the control of, the students, who paid for everything. In Paris the reverse was true; the teachers ran the show. Others were paid for by the church, and their curriculum would naturally reflect this. Still others were under royal patronage, such as the universities at Oxford and Cambridge.
The curriculum, broadly speaking, consisted of liberal arts, law, theology, or medicine. Students would enroll at the age of 14 or so, and courses would be built around the study of a single book; whether it be a book of law, medicine, etc. The liberal arts were composed of arithmetic, geometry, astronomy, music theory, grammar, logic, and rhetoric. Students who underwent the complete six-year curriculum were awarded the title of Bachelor. Those who continued their studies in law, medicine, or theology could continue on to the ranks of Master and eventually Doctor. Teachers in one school could teach at any other without examination, and the schools as a whole had a certain degree of autonomy, within the context of their financing and reputation, of course. In one famous case, striking students didn't just leave the university, they left the entire city for several years! So the universities definitely had some political and economic clout.
From an RPG perspective, not only are these universities the logical place to find sages in any one of the various specialties, but also could form a part of a player character's background or even current activities. Adding magical studies (the ars magica) as one of the core curricular subjects would certainly not be out of order in most campaign settings, and might even form the basis for starting off new parties. The rather staid "You all meet in a tavern..." could be replaced with the somewhat more realistic "You all know each other from the university, having progressed in different courses of study, but becoming good friends during that time..."
Adventures Dark and Deep game specifically, it would be completely apropos to say that bachelors would perforce have one of the various specialties within the scholarship secondary skill, or perhaps even generalship, alchemy, etc. Different universities might offer different specialties.
It certainly seems that universities could add quite an element of verisimilitude to a campaign set in a quasi-Medieval setting, as well as providing justification for previous relationships and the acquisition of new knowledge. Give it a go!