Palafox is not a Basque surname. I think that it's origin is French (but I am not sure), there has been two Palafox famous in the history of Spain

Jose Rebolledo de Palafox: Born in Zaragoza in 1776, he was a general of the Spanish Army, and senator, he is considered as The hero of the Zaragoza siege during the war of the Independence versus Napoleon

Juan Palafox Mendoza: Born in Fitero (Navarra) in 1600, he was priest, writer, and administrator of the Colonies

Athough Palafox is not a Basque name, there have been families with this surname in Navarra, and also in Aragon. These families were nobles, so I recommend that you make your genealogy, I think it will be very interesting.