I'm doing research for my book. My main character, Bayard, is a peasant. He joins the rebellion, which arranged for death of a minor noble family, (it was the only one they could kill without being slaughtered) burned and disfigured Bayard to make his face unrecognizable and sent him to court pretending to be their son. How likely is this? What are other ways for peasants to become powerful?
I think you're operating under two misconceptions. One, you're confusing the cause with the effect. A family was aristocratic because it possessed significant land; land being the primary means of production in the Middle Ages, landholders could extract wealth from their control of land. Your status as a noble might get you certain benefits, but no one is going to shower you with money and power simply because they think you were born to a good family.
The second is that, as always, social class exists on a continuum. At the bottom, you have destitute vagabond laborers; at the top, huge regional magnates. But in between, there are a lot of gradations. The "common folk" would include not only vagabonds and serfs, but free peasants who rented land for cash; minor landowners who worked their own land with the help of servants; merchants and craftsmen from towns, ranging from poor apprentices to quite wealthy men with real power. These people were rarely, if ever, united in any meaningful sense, and it's hard to imagine they felt any real unity; Marxist class consciousness is not something that's really attested to. Peasant rebellions were usually spontaneous affairs with identifiable, concrete causes: an increase in rents, a change in customary law, etc.
This was not a caste society, and the means by which a peasant could raise himself in the world then were not all that different than they are today: hard work, thrift, connection building, and a healthy dose of luck. If we're talking about a serf or something like that, probably the most likely explanation for a dramatic rise in station is that he moved to a town, learned a trade, and prospered at it.
By the by, showing up to court - whose court? - claiming to be the scion of a minor family of landholders is not going to get you wealth and power; at best, it might get you a tryout. Lords and kings were almost always in the market for military manpower, but a man with no training, and no acculturation to the ways of the military aristocracy, would be quickly discovered as a fraud.