Excuse me, English common law - which is also a foundation of our legal system - states that Jus Soli is the right and proper way to consider natural born citizenship.
And here are a few dozen references stating that English common law was the foundation of our own legal system.
Can you show any references that state that Vattel's The Law of Nations was the foundation for our legal system? I'm not denying it had an influence, but for 150 years the Americas had used English common law, it was the law that our Founders were governed by until the revolution, and it is widely acknowledged by multiple legal references (West's Law, Black's Law, etc) and our own Supreme Court and Government as the foundation for our own Nation.