Before I leap into checking relays etc etc, could the horn not working just be the result of a rusty ground?  Is this a common issue with C3's?

I really don't know when the horn last worked but I can tell you that the car sat easily for 3 years without being used.

And of course this will be needed for inspection. :|

Apologies, I will first see if the relay is clicking and go from there.

Man I have always hated troubleshooting horns..

They are very easy to remove. Take off, clean up contacts, and hook it directly to a battery. Fastest way to see if it toots. Be ready, they're loud up close!

I suspect it's the horn itself. Sometimes you can get a horn to work again by having it powered while you turn the adjusting screw in and out to see if it will start vibrating again.

I have the opposite problem, my horn goes off at random times, especially when turning after I've been driving for a while.  It's a problem inside the column which highlights the fact that there can be a number of issues affecting horn operation behind the steering wheel.  I'm in favor of checking the relay first to see if it's the horn(s) itself.  If the relay isn't clicking when you hit the horn button the problem may be in there.  But if it is clicking my bet would be the contacts on the horn or the horn itself as mentioned by others.  Good luck.