Perhaps it could have happened with a major Basque effort in the reconquista?
That's more of what I was thinking.
It might have to involve a very very bloody reconquista in which a good portion of the local populace is killed in the fighting, resulting in Basque men/women intermarrying and bringing their cultural traditions into the conquered land. Even if they get a small portion of Iberia, the butterflies from there are endless. If you have a semi-large basque state, it lays the groundwork for a larger one down the road via diplomacy, military, et cetera
Im also thinking on the Reconquista. It seems possible, especially if a more aggressive Ummayad caliphate manages to conquer the other Christian peninsular kingdoms, probably even going into France. Say if our POD is the defeat of Charles Martell at tours, we are left with an isolated Christian kingdom in the Pyrenees, in a privileged position to exploit the imminent breakdown of the caliphate. Then we can have a Basque Spain and a Basque new world, even. Since they would be more isolated than a indo-european speaking Spain due to language barriers.
That would be colorful to say the least.
It might have to involve a very very bloody reconquista in which a good portion of the local populace is killed in the fighting, resulting in Basque men/women intermarrying and bringing their cultural traditions into the conquered land. Even if they get a small portion of Iberia, the butterflies from there are endless. If you have a semi-large basque state, it lays the groundwork for a larger one down the road via diplomacy, military, et cetera