I would suspect that basque cuisines would be heavily Spanish influenced as a large portion of the basque homelands are in Spain..
That said, after a little looking it seems that while they are from Spain and southern France their language and cuisine is uniquely their own.
Lots of info out there on Basque cuisine.
Some people even believe they were atlanteans. In the basque history of the world it said way back in the day they were mainly bean eaters, distrusted root vegetables, used animal fats, and made apple cider. They learned about olives and grapes much later from the Roman’s and may also have been the worlds first cheese makers. Later they got heavy into whaling and cod fishing and may have been crossing the Atlantic for those before Columbus.
The main cookbooks from Spain and France aren’t printed in English but there’s a few. The ones I read the food was alot of seafood, cod, salt cod, chorizo, beans, peppers and pepper sauces, olive oil, salt, and appetizers on mini toasts called pintxos that often involve anchovies. Also thick cornmeal wraps to hold chorizo sausages, ciders, and seafood paella rice probably Spanish influenced. They have big bone in ribeyes as well.
The American basque food appears to be fairly different. I’m assuming due to lack of fresh seafood and other ingredients easily available back home. Cabbage soups, garlicky salads, garlicky lamb chops, steaks, halibut, beans, spaghetti, French fries, bread n butter, and vanilla ice cream to name a few. But those are what I’ve seen online at restaurants, not from homes. I’ve found a few recipes online for beans and the soup that I’ll try in the next few weeks.