Both meeting and gathering would work in your announcement.
The one difference I can tell you that may be hard to figure out from the dictionaries is that meeting has a bit more of a formal feel to it, while gathering feels less formal. (I’m not talking about the formality of language here; I’m talking about the formality of the event.)
Put another way, I go to meetings when I’m at work, I go to gatherings on the weekends with my friends.
So if your “language corner” is a formal occasion with an agenda, then meeting might be the better word to use. However, if it’s more of an informal gathering with cookies and punch served, than meeting may not be quite the right word for it. (It wouldn’t be wrong, but I sense that perhaps you want to use something “warmer” and more inviting.)
A nice alternative might be get-together, which one dictionary defines as: a casual social gathering. It’s not as formal as meeting, but it’s more recognizable than meet-up. Collins defines it as:
an informal meeting or party, usually arranged for a particular purpose
while M-W says:
meeting; especially : an informal social gathering