That's crazy. I don't know about Canadian law, but I don't understand how they have jurisdiction over the internet. I would certainly understand about any physical signs in front of the store (legally speaking), but facebook?

There are English-speaking tourists (and others, of course) in Quebec. Is it illegal to target them as a specific customer group? I don't see why she couldn't make her entire facebook page in Bosnian or Swahili either.

I think the business is not being fined because its Facebook page is in English, but because it is not also in French. Well, that's how it works for physical signs on shops: they can't display anything in English (or any language?) if there isn't also a French version of it. There might even be something about the size of the French text, which must be larger than the English version.

French and Quebecois radios also have quotas. I think in France radios have to broadcast at least 30% of French songs. I don't know about that figure in Québec.

So the business in Québec could have had no Facebook page at all, or a French page or a page written mostly in French, but not in a foreign language only...