The sauce 's name refers to the Béarn region , a former province now in the département of Pyrénées-Atlantiques , in southwestern France .
Some assume Béarnaise refers to the Béarn region , a former province now in the département of Pyrénées-Atlantiques , in southwestern Franceto refer to the region of Béarn However , the sauce has no tradition in the cooking of the area , and Larousse has the name honoring Henri IV of France , a native of Béarn , and for whom the restaurant where the sauce was first shown was named .