Yeah, there are a number of ways of telling someone how to shut up in French, (and Quebec does it differently than France). In France, this is one of the more aggressive / assertive / rude ways. But, the way he said it was a milder version, so it’s more a “stfu” rather than “shut the fuck up”.

There’s “tais toi” which is basically like “be quiet”. What you might say to kids being annoying. There’s “ferme ta bouche”, which is literally “shut your mouth”. Or, “ferme la”, which is basically “shut it”. He basically picked the rudest form, but said it in the mildest way.

Omelette au fromage s’il te plaît