I believe the founders and framers would be repulsed by such a notion.
However, in the interesting case of the heir apparent to the French Monarchy, Prince Louis Duke of Burgundy:
Point 1: 40 years, nobody in their right mind thought it possible that a person born with foreign citizenship, who is an outright Marxist America hater...would be elected President and Commander in Chief.
Point 2: 40 years from now, who's to say that the Duke of Burgundy, then perhaps the senior male heir and therefore reigning head of the Bourbon House, couldn't be elected President and Commander in Chief of the U.S. since he was, born in New York.
Point 3: Shortly thereafter, who's to say it's impossible that the French government either a) realizes an opportunity to influence our Executive branch & foreign policy or b) simply longs for a national identity with the chaos surrounding the E.U...reinstates the crown (like they've done in the past), even if it's with restrictions.
Point is, the Duke of Burgundy is 1st in line (behind his father) in royal French blood...and is also considered an American citizen because he was born here. People think it's far fetched? I would direct them back to point 1.
This goes precisely to the fears the framers had at the time. A foreign Prince/government, gaining direct access to the Presidency and the head of our Executive office.
If the 14th Amendment = NBC, then this is exactly what is possible in ~40 years.