"tabac" feels too restrictive, "Épicerie" feels more like selling fruits/vegetables, "commerce de proximité" feels like it could include things like a supermarket too.

I can think of more unsavory/xenophobic/slang terms for it, but droguerie seems more appropriate.

And on the other end for someone who never been to Québec, "Je vais au dépanneur" sounds like "I'm going to the mechanics (to fix my car)". Very creative.

this goes years back, but in the early 2000s I visited Paris and was a bit scandalized to hear the colloquial name for corner store was "l'Arabe" (!)

I rest my case.

Maybe you are right and I should have used "already existing" instead of "standard".

I'm also curious how a convenience store is called in other francophone areas of the world.

Epicerie seems a more popular option among the “traditional” options.

For example https://fr.wikipedia.org/wiki/D%C3%A9panneur says:

    Le mot dépanneur peut désigner :
    […]
    au Québec, une petite épicerie de proximité ou une supérette.
    en Suisse romande, une petite épicerie ouverte les soirs ou les week-ends.
    […]

It points to https://fr.wikipedia.org/wiki/Magasin_de_proximit%C3%A9 and https://fr.wiktionary.org/wiki/d%C3%A9panneur where again one finds mentions to epicerie (and none to droguerie).