Well, I agree that this Bass is a little mystery but the C-bouts do not look French to me at all. Either German or Bohemian actually. On the Varnish, how do you know the varnish is actually original? What if someone 20, 40, 60 or 80 years ago refinished it. Would you be able to tell? Also, not all Red over Gold = French! Have a look at
my Martini and tell me if that doesn't look similar in color as well.
The Bass is a nice looking Bass whatever it is and the Scroll is not easy to tell in Pics. I would need to have it here with a UV light and check the Varnish as compared to the Back to see if it matches. If the head is older than the possible re-finish, then it might match if it was completely stripped. If the Varnish on the Bass is original or if the Head's varnish is different under UV, then we know for sure it has been replaced. Many Basses have led a rough and tough life. Many of the types or Repairs and butchery that we have seen on some older Basses are not done much in todays world but there are some who just don't know any better so beware when having your Bass fixed by anyone other than a top class Bass luthier.
On the Elgar Pics, I can't post them for you sorry. On this Bass, I still want to see the back Button area and Purfling close-up if possible.