You are right that I downloaded an English translation of Vattel that was not available at the writing of the Constitution.
The framers were educated and could read and speak French. Your link provided the critical sentence.
Les Naturels ou indigènes font ceux qui font nés dans le pays de Parens Citoyens.
which using an online translator (since my high school French has mostly left me) =
“The natural or indigenous are those born in the country of citizen parents.”
I find it interesting that you link to a site but then do no critical thinking of the information that they present.
They make a big deal that citizen is only used once in the sentence. To me this is just an issue of how we would phrase the thought in English vs. French. It is still clear to me that the framers relied on Vattel. And Vattel defined a Natural (implied citizen) as one born of citizen parents in the country.
Good try - but no cigar for your side. But you did correct and refine my thinking so I thank you.
The "big deal" is that while the "story" may have now changed, in light of inconvenient facts, the very basis for contending that Vattel's defintion was relied upon by the Founders was the contention that he used the term "natural born citizen" - which John Jay (allegedly) copied when sending his letter recommending that requirement (whereupon a link to a later edition of Vattel's work was provided as proof). But, of course, John Jay couldn't have copied from an edition published 10+ years after his letter.
With respect to the original French & online translation to "The natural or indigenous are those born in the country of citizen parents," (a) the term "natural born citizen does not appear; and, more importantly (b) "natural" is equated with "indigenous" (i.e., native) - and another foundational claim is that "natural born" citizen means something different than "native born" citizen. According to Vattel, they're the same thing. Vattel makes no distinction here - or elsewhere - between the "natural" and the "native" citizen.