It comes from the French word for "with" and, like many Japanese loanwords, was mangled into something different before being accepted into the Japanese vocabulary.
I'm assuming it was left it as is since Nachi compares it with "couple", which replaced "avec" later on.
Quick search and it seems to be a slang from the 80s Now it's a dead language, not cool anymore and used for joke about someone out of tune with the terms or to show generation gap
Well, crud. I meant to write a note when I translated it, but I completely forgot. It's not only used here to show that Ashigara is... not young, but also because she really doesn't want to call them a couple (as that would be admitting defeat).
Yeah, just like recklessfirex said "Avec" means "with" in english. But the inclusion of the word is really weird here that it doesn't makes much sense (if I try to translate it in French) so I'm not sure what she wanted to say exactly but like Paracite, I think she doesn't want to admit that they're like a couple or something.
I have to go with the combo. It makes ashigara sound like a older out of touch spinster, and by tiptoing around the word couple, it avoids the subject that she's single. The word itself is a straight loan word for a romantic couple. It didn't take hold, or so says Japanese wiki.
it seems ashigara here is depicted as a single woman who someway often failed to get together with a guy
It's "couple".No.CastellaH-Hold up, Nachi-neesan!Y-Yes! Avec!You have to sugar-coat it a bit...Thank you, Nachi.Really, those two are just a great avec, aren't they.A-An ideal avec!Shaddup! If you want it that badly, go buy it yourself!ADMIRAL! I said I wanted baumkuchen, didn't I?!"Avec" is a dead word.