Miller,
I'm pretty sure someone in France would have given me that name to call the part. I can't remember. I have seen numerous Darnes with a broken "Bolt spring", to use your terminology, which, renders them useless. Darnes with broken "Firing Springs", again, using your term, soldier right along.
Here in the states, I guess we can call them whatever we want to.
Last Dollar,
If I had a dollar for every time someone called me, with some problem they brought upon their own Darne or Charlin, themselves, usually involving a quest for unnecessary maintenance or lubrication, I would literally be a rich man. You, figuring "it didn't need to come apart" may be the most intelligent statement I have ever seen a lay person type about a sliding breech gun.
Bravo, my man. Bravo indeed.
Best,
Ted