I work in entirely different career field but we had an incident of someone cursing at people, he was written up and suspended for 3 days. He is being fired now actually, but not just for that one incident. Usually it’s an escalation. Warning, write up, suspension etc

I don’t know what policies you have, I’d think this person needs to be suspended with no pay.

Not sure about being fired but that’s a possibility. Usually retail and food service has low tolerance for bad behavior in front of customers