Okay. Yeah they know. Peasant is not an insult, it's a neutral descriptor. And they know it exist because they know that even if they represent the vast majority of the population, there are people that do not live like them. Even if rural community are relatively isolated (compared to a town) they're not completely cut off from the world (the stereotype of the village man who never saw anyone that wasn't from his village is nonsense). They pay taxes to their lord and/or the king, that means a tax collector (and the lord itself). Their priest is educated in a neighboring city and rarely from the village itself. They sell their products to a market town where they meet people from all other... they are in contact with the wider world.

So yes they use the term or local equivalent... when talking of themselves in relation to other groups. "We, peasants, are not like you city folk", that kind of things. Otherwise if they have to use a term they use the name of their village ("we are the people of St Johnston up Avon" or whatever). Just like if you live in a city nowadays you're more likely to say "I'm from Manchester" rather than "I'm a city dweller" unless you have to specify in context.

A French or Anglo-Norman noble referring to peasants might call them villeins. Though villein tended to be specific to serfs (rather than free peasants), most peasants in France, the Holy Roman Empire, Italy, northern Iberia, and post-1066 England were serfs.