It's basically savate. The majority of Basque live on the border between France and Spain so you'll see influence from both countries. From the one tape I saw of it, it looked like a cross between savate and flamenco. The stance was a bit less relaxed than savate and there was a lot of stomping to the opponent's foot along with kicks to the shin.
Again, I've only watch an hour or so of it so I'm no expert.