That means that "natural born citizen" carries with it the common law jus soli principle of England, NOT the continental rule suggested by Vattel.
Our Founding Fathers rejected English interpretations in favor of Vattel's every chance they had.
You've neglected to give any example to support your assertion.
As I look at the Framers and Vattel, it's very clear the Framers rejected many positions advocated by Vattel. For example:
§ 114. Freedom of philosophical discussion.
I speak of the freedom of philosophical discussion, which is the soul of the republic of letters. … I know that liberty has its proper bounds –” that a wise government ought to have an eye to the press, and not to allow the publication of scandalous productions, which attack morality, government, or the established religion.
Vattel is at odds with our Constitution's First Amendment protections of speech.
And:
§ 127. Of religion internal and external.
Religion consists in the doctrines concerning the Deity and the things of another life, and in the worship appointed to the honour of the Supreme Being. So far as it is seated in the heart, if is an affair of conscience, in which every one ought to be directed by his own understanding: but so far as it is external, and publicly established, it is an affair of state.
§ 129. Public establishment of religion. But we should take care not to extend this liberty beyond its just bounds. In religious affairs a citizen has only a right to be free from compulsion, but can by no means claim that of openly doing what he pleases, without regard to the consequences it may produce on society. The establishment of religion by law, and its public exercise, are matters of state, and are necessarily under the jurisdiction of the political authority. If all men are bound to serve God, the entire nation, in her national capacity is doubtless obliged to serve and honour him (Prelim. § 5), And as this important duty is to be discharged by the nation in whatever manner she judges best, –” to the nation it belongs to determine what religion she will follow, and what public worship she thinks proper to establish.
Vattel advocated that the State had jurisdiction over public expression of religious belief and even advocated there be a state religion. The Framers rejected both notions.
And:
§ 176. Means of putting a stop to this disorder.
* * *Since it is an established custom that the nobility and military men should appear armed, even in time of peace, care should be taken to enforce a rigid observance of the laws which allow the privilege of wearing swords to these two orders of men only
Vattel advocated against a general right of all persons to bear arms. The Framers rejected Vattel here.
There are many more examples like these, which make it very difficult to sustain the argument the Framers paid much deference to Vattel.
Since the Framers rejected Vattel's ideas on many matters, why should it be supposed they incorporated his ideas on citizenship? The notion fails for want of evidence.
That's not true. The English Bill of Rights of 1689:
"...subjects which are Protestants may have arms for their defence suitable to their conditions and as allowed by law."
Vattel:
"Since it is an established custom that the nobility and military men should appear armed, even in time of peace, care should be taken to enforce a rigid observance of the laws which allow the privilege of wearing swords to these two orders of men only."
Which one of those sounds more like the Founders' opinion?
“Our Founding Fathers rejected English interpretations in favor of Vattel’s every chance they had.’
According to Alexander Hamilton to determine the meaning of terms in the Constitution, we should look to the English legal system.
“...where so important a distinction in the Constitution is to be realized, it is fair to seek the meaning of terms in the statutory language of that country from which our jurisprudence is derived.” 1795