Yup, this is french influence from the old days. Very common in Sweden and Finland, both colloquial and formal language. Apparently short for 'du café avec le petit verre'. Nowadays 'avec' has turned into a proper noun in our languages and is treated as such, people can say things like "can you fetch the avec?"

In some parts of Finland 'avec' has a second usage, corresponding to the english term 'plus one' on invitations. At some point in time FInnair lounge pages actually just said 'avec' instead of describing guest policy in detail!