My husband was born in Toule, France in 1958 while his father (US citizen) was in the US Air Force. His mother (US citizen) gave birth in a France hospital (name unknown), not on the base.
Both parents are deceased. My husband does not have any documentation (birth certificate, etc) proving his naturalized citizenship. How can he go about obtaining it?

First of all, he needs to get certified copy of his birth certificate. Without this document, he cannot claim US citizenship.