Navarre was generally leaning towards being a part of French geopolitical ensemble from the XIIth century until the XVth. It's arguably especially the case because of a matrimonial policy which favoured these links, but these marriages didn't were decided out of the blue.
Basically, Navarre had a pretty much tensed relationship with Castille-Leon (which were allies/rival in this stage of Reconquista) and especially Aragon (whom kings tried to stress their suzerainty on Navarre), it grew with increasingly better relationship with Pyrenean, Aquitain and eventually French relationship where he could find some support (arguably, would Henry II be even more of a control maniac, it would have been short-lived).
As
@Analytical Engine pointed, the marriage between Richard and Berengaria (which brang the ever-broke Richard a rich dowry) can be explained as such. Still, you don't just pull claims out of the blue, just by having a marriage with the royal dynas...
nevermind.
A personal union is likely with an Anglo-Gascon marriage with whoever rules Navarre, but you need to prevent the House of Chamapagne and of course Capetians to have a go at it. Maybe Sanche VI having a son would be helpful. I wouldn't see this union last to becoming an absorbtion but something like Capetian Navarre, as in a cultural and political influence.