Nationality in the Ancien Regime
The term “nationality” was not used in the Ancien Regime. However, there was a tradition and understanding of who was French (Regnicole) and who was not (etranger; aubain).
The former was someone born in the kingdom or under the obedient lordships (vassals) of the king (jus soli) and who remained inside the territory of France–that is to say–did not permanently leave France.1
The nationality laws of the Ancien Regime favoured jus soli, and jus sanguinis could not be used to claim French nationality until the 17th century, and this was only if they received letters of naturalisation from the king.2
[Update: Here is an additional article which mentions letters of naturalisation and certain persons typically exempted from the right of aubaine. The article makes mention of the “ancient domains” of France, which, given the areas mentioned, implies parts of the Frankish Empire. This seems relevant because the 16th century Kingdom of Navarre was part of the both the Frankish Empire and West Francia, the precursor state of France.]
[Further Update: this book (p. 105) mentions a court decision by the Parlement of Paris in 1505 that declared subjects of Bearn to be naturally French. This was before the birth of Henri in 1553. This is complete and utter proof that Henri IV was not a foreigner.]
Henri IV, a Frenchman
In 1548, Antoine de Bourbon married Jeanne of Navarre under the orders of King Francis I. Both Antoine and Jeanne were French vassals.
The marriage produced the future Henri IV, who was born in Pau (then part of the “Kingdom” of Navarre) in 1553.
Navarre was, despite its general autonomy, a de facto vassal state of France under the rule of French vassals (and had previously been in personal union with the French Crown).
Thus, Henri IV was the product of a marriage done under royal orders and was born in a territory ruled by French vassals. This means Henri IV was French, not a foreigner to be subjected to the droit d’aubaine.
Further Antoine de Bourbon was made Admiral of Guyenne3, an office which Henri would later inherit with the death of his father.Ibid. This would not have been allowed had Henri been a foreigner under the droit d’aubaine.
Thus, it must be concluded that Henri IV, being born of French vassals in a French vassal state, and being allowed to inherit French titles and offices was not a foreigner.