This mirrors the Vatel/Law of Nations definition.
"The natives, or natural-born citizens, are those born in the country, of parents who are citizens". In the original French, IIRC, the terms were "indigenes o naturales". (Pardon the spelling and lack of accent marks). Even though I can't read French, many of those who wrote the Constitution could, and had both an earlier English translation and the original French versions at hand.
Regarding the original French version:
""Please note that the correct title of Vattel's Book I, Chapter 19, section 212, is Of the citizens and naturals. It is not Of citizens and natives as it was originally translated into English. While other translation errors were corrected in reprints, that 1759 translation error was never corrected in reprints. The error was made by translators in London operating under English law, and was mis-translated in error, or was possibly translated to suit their needs to convey a different meaning to Vattel to the English only reader. In French, as a noun, native is rendered as originaire or indigene, not as naturel. For naturel to mean native would need to be used as an adjective. In fact when Vattel defines "natural born citizens" in the second sentence of section 212 after defining general or ordinary citizens in the first sentence, you see that he uses the word "indigenes" for natives along with "Les naturels" in that sentence. He used the word "naturels" to emphasize clearly who he was defining as those who were born in the country of two citizens of the country. Also, when we read Vattel, we must understand that Vattel's use of the word "natives" in 1758 is not to be read with modern day various alternative usages of that word. You must read it in the full context of sentence 2 of section 212 to fully understand what Vattel was defining from natural law, i.e., natural born citizenship of a country. "
http://www.thebirthers.org
Translating the french text: "les naturels, ou indigenes, sont ceux qui sont nes dans le pays, de parents citoyens"
To English, gives this: "the natural, or indigenous, are those born in the country, parents who are citizens"