Really? And what "French law" exactly?
Guy was referencing Vattel, who wrote about civil law, which was based on old Roman law.
The US Constitution and US laws in general are based rather in common law, an almost entirely separate code based on centuries of English judicial decisions.
The common law definition of how one becomes a citizen is quite different from the civil law definition.
IMO the Founders intended the normal, common law definition of legal terms unless they explicitly state otherwise.
Sorry, I made a mistake, Swiss, not French. The Laws of Nations was a given set of laws in Europe at the time that those nations, specifically the English, used as almost a baseline for their own interactions.
US Law however, is based on Common Law, not the “Laws of Nations” which was an old offshoot of Roman Law (if my memory of the history of it is correct).