Vattel was the key in the United States Constitution in determining the Article 2 Natural Born Citizen clause. Here is a list of the references used by John Adams, Thomas Jefferson, and George Washington in regards to Vattel’s Law of Nations. This should dispel any notion that the Founding Fathers did not use the Law of Nations as their guide.
Vattel – John Adams

Section 212 from Vattels Law of Nations, which was referenced by the Founding Fathers, not Blackstone who was British. Remember we had just defeated the Brits in a war and we did not use their tyranical laws…we used French Varttel.

§ 212. Citizens and natives.

The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights. The society is supposed to desire this, in consequence of what it owes to its own preservation; and it is presumed, as matter of course, that each citizen, on entering into society, reserves to his children the right of becoming members of it. The country of the fathers is therefore that of the children; and these become true citizens merely by their tacit consent. We shall soon see whether, on their coming to the years of discretion, they may renounce their right, and what they owe to the society in which they were born. I say, that, in order to be of the country, it is necessary that a person be born of a father who is a citizen; for, if he is born there of a foreigner, it will be only the place of his birth, and not his country.

Read what the Founders read and referenced for our Constitution: http://www.constitution.org/vattel/vattel_01.htm