A few years ago, I spent some time reading French and Spanish sources on the origins of Jean Salazar, who is important for living descendants of early Acadian colonists in New France, and to living descendants in old France (and elsewhere). I made a lengthy comment here on his profile, with my draft sketch of a possible descent, based on that reading and assessment of a) prior secondary sources, some linked, and b) certain recurring family names and relationships.
I am not not working on this at present. Escalating here to G2G in case somebody else, and this may be helpful. Please consider as hints and clues, not assertion.
Note this goes back pre-1000, so, suffice to say: we'll (probably) never know.
Respectfully, your cousin somehow
p.s. Do we have a Basque project?