The old Motobecane that I had used a one piece dropout and hanger. If your cousin cut the hanger away then there is no real option but to get a whole new dropout and have it brazed into place. There's always welding on a cut off hanger from some other dropout but unless you're willing to carve the metal to shape with various metal working tools to match the original then it seems as if you're doing a disservice to the intent of the project.

And if your goal is to restore the bike then why would you not want to replace all the brazeons that were removed? I'm sorry but this seems like the sort of thing that is worth doing right if you're going to do it at all. And that would mean a full on restoration. How will you make this look like it was without replacing the brazeons and cable stops?

Actually from re-reading your original post it sounds like you should just drop it and buy a bike of your own to ride since that seems to be more what you're after. That way you'll have current technology and parts and won't be restricted by the oddball french threadings or period correct parts that may cause problems.