[GilesB]

So the child of a US citizen serving in the US Embassy in London or Paris, and born in the London Maternity Hospital or the American Hospital (in Paris), would not be eligible to be president?

These hospitals are considered by many to be the finest in their respective cities for childbirth, and could well be part of the carefully made plans of a US diplomat. I don’t think the embassy would maintain a full-service medical center in either of these dities.

[Jeff Winston]

So the child of a US citizen serving in the US Embassy in London or Paris, and born in the London Maternity Hospital or the American Hospital (in Paris), would not be eligible to be president?

Yep. That's another of the logical consequences of the "both-and" doctrine of natural born citizenship.

You can add all the children of US military troops serving overseas into that as well.