Why do you think that “droguerie” is the standard French word for “convenience store”?
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.
I'm also curious how a convenience store is called in other francophone areas of the world.
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).