Briefly, yes, legal treatises regarding the Law of Nations exist from many centuries throughout the history of international relations. While Vattel’s work was not the singular source utilized by the Founding Fathers, they did indeed remark on numerous occasions about using it as an important source for their legal research for the Constitution and other legal activities. Several Supreme Court decisions have acknowledged Vattel as a source for the law regarding citizenship. It takes time to assemble the citations, but they do esit. Leo Donofrio and others have cited a number of the sources for anyone who wants to take the time to consult them.
Here is some reference provided by Attorney Apuzzo's court documents:
"THE VENUS, 12 U.S. (8 Cranch) 253, 289 (1814) (Marshall, C.J. concurring) (cites Vattel’s definition of Natural Born Citizen)
SHANKS V. DUPONT, 28 U.S. 242, 245 (1830) (same definition without citing Vattel)
MINOR V. HAPPERSETT, 88 U.S.162,167-168 ( 1875) (same definition without citing Vattel)
EX PARTE REYNOLDS, 1879, 5 Dill., 394, 402 (same definition and cites Vattel)
UNITED STATES V WARD, 42 F.320 (C.C.S.D. Cal. 1890) (same definition and cites Vattel.)"