No. The Basque language (Euskara) is primarily spoken in the Basque Country, a cultural region straddling the western Pyrenees and the Bay of Biscay. This area spans:
Spain (the majority of speakers): provinces of Gipuzkoa, Biscay, Álava, and Navarre
France (a smaller portion): the Northern Basque Country (Labourd, Lower Navarre, Soule)
The vast majority of Basque speakers reside on the Spanish side.