Karen, just spotted this.
No, the after hours numbers are not restricted to big cities. I live in Lozere and you don't get more rural than that. Lozere has such a number as I said in Useful Links/Emergency! .
The local fire brigade is the ambulance service so far as I know. It's certainly the case here and it was also the case when I slipped on some steps in Paris and ruptured my quadriceps tendon. In a major emergency the SAMU will also send their own emergency vehicle staffed by specialists, including a doctor I believe. But in rural areas they can be some way away (ours is 37 km away, while the fire brigade is 5 km from us).
Like Brian, the local firemen and women greet me as an old friend and all ask me how I'm getting on.
I'm sorry you couldn't find your department's number with the Google search I suggest. Ask your doctor, the chemist, the mairie, the prefecture, even the fire brigade. Have you looked in your local newspaper? Ours has a regular box item with all the emergency numbers. If yours doesn't, you could call them and ask them why not. And ask them at the same time what the number is!
It may also be the case that your department hasn't set up this service but I have no information on that.
If you call 15 for the SAMU and it's not an emergency they will put you through to the on-call doctor. But your call may be blocking someone who has a real emergency. Which is why in the UK they introduced the second-level 101 and 111 numbers. And it's why I believe people should make the effort to find these special non-emergency numbers and use them. (Gets down off high horse trying not to fall and having to dial 15).