Aren't these delis? At least when I used to live in Brooklyn we used to call them that. Often they had signs "Deli and Grocery" or something like that.
Milkbar in Australia because they used to sell milkshakes and the convenience store aspect was secondary. Over time the convenience store part took over but the name stuck.
"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.
God forbid the language evolves independently in two regions separated by an ocean.
I find it funny that in France it’s more common to see anglicisms (parking, le weekend) whereas in Quebec more “francized” terms are more common (stationnement, fin de semaine). And then Francois Legault goes and in a speech praising the work of the French language watchdog says “faut faire la job”. Facepalm!