I was wondering how far back in history people in the Middle Ages knew about. Obviously, they knew of the birth of Christ, but how much did they know of the Romans and their history? What of the Greeks? Would our hypothetical scholar know who Alexander the Great was, or know of the Peloponnesian War?
You might be interested in the 1493 Nuremburg Chronicle, known as one of the first "books."It's a little after your date, but shows extensive knowledge of classical history. Here's a good English translation; the site also has good images of each original page. You'll want to look at the 7th age.
As you can see, classical history was never really lost. The main reason we have so many Roman and Greek texts is because scholars of yore have found them worthy of keeping around. In fact, you can find several authors you might have heard of illustrated in the Nuremburg: Suetonius, Herodotus, Tacitus, etc. If it weren't for medieval monks and scholars, we wouldn't have their classic works around.
Dante, who wrote in the 1300s mentions certain "virtuous pagans" in his Inferno. Mentioned among others are the greek philosophers Plato, Socrates and Aristotle, the doctor Hippocrates and the poet Homer. He mentions certain Romans including Cicero and Julius Caesar.
Since he knew of Homer who lived in the 8th century BC and of the Romans of the late Republic who lived in the 1st century BC, so it is possible that he knew of the events and the figures who lived in this time span.
Given that Dante wrote about these people, we can assume that his audience would have been familiar with at least a few of these names.
As for whether someone from that era might know of Alexander the great in particular the answer is yes. We know this because of a 12th century epic poem by Walter of Chatillon called Alexandreis. The poem is a mythical account of the life of Alexander.