I'm ashamed to be french when I see this kind of horse shit.
The internet is not compatible with their TOS.
I've seen Frenchmen ashamed to be French when a Le Pen won something somewhere. I've seen Frenchmen ashamed to be French when an anti piracy group pirates a logo. I've seen Frenchmen ashamed to be French when some president felt the need to compensate for something by blowing up a nuclear bomb in the pacific.
Somehow, anecdotally, being ashamed to be born somewhere is a particularly French phenomenon. Why?
France has all the above things, but also a great healthcare system, nice people, a somewhat functional democracy, and many other great things.
There's 60 million Frenchmen. Are you going to be ashamed every time one of them does something wrong? Do you expect them to be ashamed every time you do something wrong?
Instead of shame, maybe it would be more constructive to organize and do something about it. The ivory tower of the French political elite is notorious, but not unsurmountable.
Yes, we should be ashamed when someone does something wrong. In fact, we shouldn't be ashamed to be ashamed of some dumb decision. Being ashamed doesn't mean we are not doing anything else about it. You've seen Frenchmen being ashamed to be French, and that's OK. It means they're not thinking their country is the best, but they can also learn from their mistakes. And I am proud of this, as a French person, too, though I am ashamed of LeBonCoin's strategy.
I agree there's nothing to be ashamed here, especially as leboncoin position is quite understandable (and their tone not that menacing).
It's a pretty common thing across every culture where people attribute the bad things that happen around them to the geography or culture when in reality, there are crappy drivers all over the world.
No need to, it's just plain old cheap lawyer tactics, it's been around since the beginning of time:
Scare people (i.e. by making them feel they're in danger) and they will do what you want. (Law seems complicated to non-lawyers, so lawyers make use of that, basically by communicating "I'm the specialist and you don't know anything about this domain, so do as I say")
In the case of this story, all I'd suggest the owner of the app, to steer clear of legal issues, is:
a) don't use their name,
b) don't use their logo (or other very distinct parts of their Corporate Identity)
c) re-launch your app (using proxies)
EDIT: On second thought - they don't deserve your exclusive traffic/promotion/value you add. If you keep your app alive, you should multiply your sources (add as many similar sites as possible).