According to the Wikipedia and other folks, the Cagots don't appear to have any unifying ethnicity or origin, were not linguistically or religiously different from anyone else and were identified as Cagots primarily by virtue of being born Cagots. Cagots were excluded from mainstream French and Spanish society, lived in their own towns, were restricted to certain professions and churches had segregated Cagot and not-Cagot sections.
The Cagots do not seem to have done anything to deserve their treatment; even if they were descended from lepers (which seems highly unlikely) or later Christian converts, or an assortment of originally ethnically distinct folks clustered in/around the Pyrenees, this hardly justifies matters. The only accusation I have seen levied against them is drinking, and that hardly differentiates them from everyone else in Europe.
Today, the Cagots have all but disappeared, most likely into the general French and Spanish populations (and New World colonies.) The historical record is probably unlikely to make a lot of sense on this subject any time soon, but it just serves to show how much conceptions of ethnicity and group and belonging can change over time, and how un-monolithic things generally are.