According to Dictionnaire etymologique des noms de famille et premoms de France
Dauzat, the French surname Marat normally indicates one's ancestors came from a place in the Puy-de-Dome area of France
. However, in the case of the famous revolutionary Jean-Paul Marat, his name is a "Francization" of the Sardinian surname Mara
, as his father was from Sardinia. The revolutionary's family in turn claimed that Mara
was originally a surname from Spanish nobility, but Dauzat thinks a Jewish origin is more likely. But in either case he doesn't give an original meaning.