There are many arguments that the framers meant exactly the opposite of "English law."
The framers of the Constitution were, of course, well-versed in the British common law, having learned its essential principles from William Blackstones Commentaries on the Laws of England. As such, they knew that the very concept of citizenship was unknown in British common law. Blackstone speaks only of birthright subjectship or birthright allegiance, never using the terms citizen or citizenship. The idea of birthright subjectship is derived from feudal law. It is the relation of master and servant; all who are born within the protection of the king owe perpetual allegiance as a debt of gratitude.
According to Blackstone, this debt is intrinsic and cannot be forefeited, cancelled, or altered. Birthright subjectship under the common law is thus the doctrine of perpetual allegiance. Americas Founders rejected this doctrine.
The Declaration of Independence, after all, solemnly proclaims that the good People of these Colonies. . . are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved. According to Blackstone, the common law regards such an act as high treason. So the common lawthe feudal doctrine of perpetual allegiancecould not possibly serve as the ground of American (i.e., republican) citizenship.
While, obviously, the Signers and their allies intended to sever allegiance to the Crown, they did not intend to throw out all English law, or all definitions of terms based on English law. As far as I am aware, the original 13 states uniformly follow the doctrine that the common law of England continues to be the law of the state unless modified or repealed by a constitution or statute. Where our good forefathers intended a new meaning, they were not shy about saying so. The law of England as to citizenship was not derived simply from feudal doctrine, but had been established by laws passed by the English Parliament.