The personal union ended when Philip V to be King of France over Joan II of Navarre.
Joan married Philip of Évreux, putting the Navarrese throne under the French House of Évreux.
The Navarrese throne then passed to the Spanish House of Trastámara before passing to the French House of Foix.
The Navarrese throne then passed to the French House of Albret.
In 1548, Joan III of Navarre of the House of Albert married Antoine de Bourbon, putting the Navarrese throne under Bourbon control.
Thus, it could be said that Navarre was a kingdom-in-name-only.
Navarre, of course, was not the only vassal in the history of France. Normandy, Anjou, Aquitaine were also vassal states, just to name a few. Despite often being semi-sovereign, these states were considered French. The same applies to Navarre.
Like the rulers of other vassal states, the right of aubaine was never applied to them simply for ruling, living in, or being born in these vassal states.
From this, it must be concluded that Henri IV, being king-in-name-only of a French vassal state, was not considered a foreigner.
The Parlement of Paris would later rule that Navarrese would be considered French and not subject to the right of Aubaine. The exact date of the ruling is not given, but the author died in 1622, and the wording indicates that Navarre had not yet been incorporated into the French Royal Domain, which happened in 1620.