Some weeks ago I addressed a similar question about medieval knowledge of history:
I would want to add here that the divide between biblical and historical knowledge is not very clean cut. When we read the medieval sermons we can see peppering of non-biblical historical references. This is not to say these were history lessons, nor accurate, but certainly informed by broad and varied historical sources. Certainly by the time of Lateran IV (1215) with its over-arching concern for pastoral care of the laity, these sermons were produced by literate, well read monks who were engaged with theologians and Paris masters exposed to broad historical sources. These monks were also producing immense chronologies stretching across landscape and time, and these were at times sources of allegorical history for preaching.
So, we account for peasant's knowledge of history in two ways:
Bible-as-history, which it was and is.
Sermons containing extra-Biblical historical references of varying degrees - Roman, Greek, Antiquity right up through contemporaneous history - aimed at moral instruction and not knowledge of history per se.
Beyond this, I suspect history, legend, and myth (and song!) combined and passed down. But we cannot be certain how much and what. The sources we have are aristocratic and ecclesiastical.
This is a slightly peculiar way of looking at it, but Marc Bloch in The Historian's Craft suggests the very notion of time and memory, in a psychological sense, was different in the medieval period in a way that historians have to understand before approaching the actual facts of the time. This links a little to idjet's excellent answer to do with the Bible, so that history as we know it existed in an entirely different framework.
Perhaps the issue should be less how much history did peasants know (which could roughly be covered by looking at the history of education in specific countries as well as the history of history and epistemological philosophies of the time) but more how the issue of time and self-placement within history was dealt with. Bloch's work, as well as other pioneering Annales school writers who were often fond of such questions and were very often Medievalists, may be of some use.