Law of Nations was published in 1757 well before the Declaration of Independence, the Revolution, or the Constitution. While it was written in French, at that time French was spoken and read throughout the old and new worlds much as English is read and spoken throughout the world today.
England’s Common Law is law by custom and unwritten whereas America’s laws are statute or written law.
While there is some semblance to English law by custom in America laws are codified.
That's fine, but I don't think anyone can deny that Blackstone had as significant an effect on the Framers as Vattel.
My argument is with those who bluster confidently that it was clearly Vattel's vision, or Blackstones's, when it isn't clear at all - it just suits their argument.
I don't think it matters much either way since the Constitution says what it says and there's a body of precedent to guide the interpretation.