How do you know? More importantly, why does it matter? With original meaning, you need only answer, "What would a reasonable person living at the time of ratification have understood these words to mean?" Intent doesn't factor in.
Given that a reasonable person in the United States of 1788 had been a "natural-born subject" of the British Crown prior to 1783, it seems exceedingly unlikely that he would understand "natural-born citizen" based on a specific English translation of de Vattel's French writing.
It is super simple. Citizenship is whatever the sovereign commands the allegiance to be. Whenever two sovereigns dispute the allegiance owed to them by a person, that person may suffer terrible consequences.
Natural born citizenship is based upon the allegiance owed to a sovereign at birth. When the sovereign commands the allegiance owed at birth to be determined by the allegiance of the father, then the natural born citizenship of the newborn child is that of the father as observed by Vattel. When the sovereign commands the allegiance owed at birth to be determined by the sovereign of the domain in which the birth occurred, then the natural born citizenship of the newborn child is that of the domain to whom the child owes allegiance at birth.
The United States in 1961 recognized the allegiance of the child at birth to be that of the adult father or adult parent, while reserving the possibility the child could elect to renounce natural born foreign allegiance and natural born foreign citizenship upon reaching the majority age of an adult and thereafter exercise only U.S. native born citizenship.