His comment, from his own Swiss point of view, was that the natives, or indigenes (we would say the "indigenous people" of a country) were those born in the country of parents who were citizens.
His book was never the source of our phrase natural born citizen (which came from natural born subject), and no one ever translated his "natives or indigenes" to mean "natural born ciitizens" until 10 years after our Constitution was written.
When they did, it wasn't even an American translator who used that phrase. It was some guy over in England.
Vattel has nothing at all to do with "natural born citizen" in our Constitution. And yes, if Ted Cruz was born an American citizen, he's eligible to be elected President.
The writings of Founders and records will show that Franklin and Washington and probably others were well aware of Vattel and it was Franklin who had copies of Vattel’s books who suggested that the drafted Constitution be revisited to incorporate the the Founder’s intent to have a ‘natural born citizen’ as a requirement for POTUSA. Cruz being born and resident in Canada for four years of a USA citizen mother and a Cuban father does not meet the POTUSA requirements as far as I am concerned. It can be argued that the USA shorts Itself from very able and really Constitutional people by the Founders use of words but I believe the Founders were men of wisdom beyond their times and did their best to lay out a document ‘to form a more perfect union’ for generations to come. There are and will be men and women to carry the Founder’s intentions.