If anything, we can joke that Navarre ruled the basques, to the point that biscayans, under the their Haro dinasty lords, allied with the leonese-castilians against Pamplona. But maybe your question is more aimed towards ethnic/cultural compositon. Historically, the navarrese kingdom was a pluricultural entity (as almost everyone else in the Middle Ages), it would be an error to pretend to understand it in the more "monolithic" cultural and institutional categories we use in the time of the Nation-States, though obviously basque culture is very important there (as a native navarrese culture, not an exterior imposition or influence). Linguistically, occitan, french and, principally, aragonese are present besides the euskera, with the aragonese being widely used by the Court. The geographical distribution of aragonese and euskera in the navarrese territory broadly matched the current distribution of euskera and spanish.
You have to take into consideration also that euskera is not a unified language until more recent times, but a set of dialects, sometimes hardly mutually understable.
Most important, in the same sense, and coherently with the aforementioned difference of identitary concepts before the surge of nationalisms, you can`t project modern idea of basque identity in medieval Navarre, nor in the vascongadas so, summarizing, there is a large part of Navarre that is basque-speaking (actually this is, aparently, the original territory of the vascones) and and it plays a main role in the navarrese kingdom, though is not exclusive not necessarily solidary with other basque territories which always seeked and defended a large degree of local autonomy and that are oeprating in a world where corporative, dynastic and/or feudal interests prevail in political infighting over other considerations.
EDIT: Well, Falecius nijaed me. Though is the spanish constitution that allows a basque-navarrese union.