Entrance varied dramatically by time and place, with students enrolling at Oxford or Paris around the age of 14 to study the liberal arts, and at Bologna around the age of 30 to study law.
Historically the curriculum of a liberal arts degree was first the study of the trivium of grammar, rhetoric and logic, followed by the quadrivium of arithmetic, geometry, music and astronomy. During the Renaissance the curriculum expanded to include the Aristotelian sciences of physics, metaphysics, and moral philosophy.
All studies were in Latin, though Greek might have been used for the study of Euclid's geometry, and later for the study of the Aristotelian sciences. Note that the initial trivium, taught in Latin, was actually the study of Latin grammar; of Latin rhetoric, and of Latin logic. and thus was the study of first the written language, the spoken language, and then of constructing written and spoken argument in the language.
So far from requiring a solid knowledge of Latin prior to entrance, the first few years of a student's studies were devoted to its mastery: written; spoken; and as a means of analytical thought. Of course to be recognized as a candidate for sponsorship at one of these institutions a young boy would likely be demonstrating aptitude in the language.
For the southern universities modeled on Bologna, studying for an advanced degrees in law, medicine or theology would have as prerequisite prior knowledge of the liberal arts.
Note that the founding of Oxford( teaching 1096, recognized 1167) and Cambridge (1209) precedes the founding of Eton College (1441) by hundreds of years. The concept of a grammar school, where one might begin the study of the first of the liberal arts at a younger age and prior to entering university, post dates the concept of university by centuries.