And you can bet the founders knew it too. Over and over we see examples where they relied on the important, contemporaneous works of the day, Adam Smith, John Locke, etc.
Vattels “Law of Nations” is THE treatise on international relations and obligations.
But Blackstone's Commentaries was THE work on English common law. And Blackstone says that a child born in England was a natural born English subject regardless of the nationality of the parents. Don't cherry-pick Vattel and pretend that the whole world agreed with him on the subject.