A French-English dictionary contemporaneous with Vattel defines Les Naturels François as "The French Natives."
I've seen no reason to believe anyone reading the original French version (or English translations available at the time of the drafting of the Constitution) would get "natural-born citizen" from Vattel's Law of Nations.
<>I’ve seen no reason to believe anyone reading the original French version (or English translations available at the time of the drafting of the Constitution) would get “natural-born citizen” from Vattel’s Law of Nations.<>
Historian David Ramsay did, along with Vattel’s definition thereof in 1789:
And Justice Waite in his Minor v Happersett identified “natural-born citizen” as a synonym for “native”, along with Vattel’s definition therof, as derived from common law when he wrote:
“At common law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children, born in a country of parents who were its citizens, became themselves, upon their birth, citizens also. These were <>natives, or natural-born citizens<>, as distinguished from aliens or foreigners.
http://www.thepostemail.com/2009/10/18/4-supreme-court-cases-define-natural-born-citizen/