"I don't know what happened to his wife, she isn't mentioned in the will and estate proceedings nor were any children mentioned. She might've died or they might've divorced before he left New York."
Louisiana succession (probate) is pretty unique. They usually start off with a discussion of family. (e.g. "Was married but once, to XXXXX, which produced three children, XXX, XXX, XXX.") This is due to forced heirship by which the spouse and children are each assured a minimum cut of the estate. If the succession does not mention wife or children, either he didn't have any or had been hiding the fact.
If the family has not been keeping the tomb up since 1816, I would not expect to find very much.