They had no formal education, no TV documentaries and no Wikipedia. Outside of their daily work, how much would a Western peasant have known about the political state of their surroundings, their history and what lay beyond the sea?
Is it conceivable that an English farmer may have been quite aware of Egypt and Russia?
They would have at least know of Egypt and the Levant as they would have been preached to them by the bishopric on behalf of the Pope in order to gain support for the crusades. The Medieval Period is quite large don't forget. It would certainly have depended on what was going on in the world around them. Many peasants went on the first crusade (where many of them died) as unarmed pilgrims - so those that returned would have known of France, Italy, the Byzantines, Anatolia (Turkey) and the Levant.
Men that fought in the 100 Years' War would have known of parts of France and England as they would have marched through it.
We can't expect that the general peasant or serf was an idle minded dimwit. Expect them to have the same brain capacity as most average people today and it will help you get a better idea.
Churches would have taught people much of the layout of the land, and news was always carried across the county. Local villages would certainly have had knowledge of the larger cities in the country as Kingdoms became more centralized (that is the power goes more to the king and his government as opposed to his vassals).
Peasants wouldn't have known, then about the outside world unless they'd personally seen it (which would have been rare) or unless someone had directly taught them about it like in the Churches. They would have know that Jesus was from the Levant but probably couldn't have pointed it out on a map if that's more along the lines you want to know? They would have known their immediate histories as not many peasants would have been well-read and would have relied on word-of-mouth history instead.
EDIT - added something I forgot to mention
The best sources for this are court records, and records from the inquisition. Some of these have been collected together in a brilliant book called The Cheese and the Worms which reconstructs the life and worldview of a 16th century miller. There was a local school nearby which the miller may have attended. In any case he appears to have been remarkably well read, and knowledgeable of the world around him.