Well, so as french I can say you are only party true. Chou do really means cabbage (choux is for plural). What bothers me in the name of the perfumery shop is that it seems to be written in 2 words. Mon chou chou. A ’chouchou’ can be many things first it can be the favorite student of a professor (talking about first classes of school from grade 0 to 7) it has almost a pejorative sense cuz the one called ’chouchou’ by the others students is not very well perceived or liked by them . It can also be a fabric-covered elastic used to tie hair into a ponytail (and if I remember well Ms Lee is wearing such a thing). And third chouchou can be a sweet candy made with peanuts covered with melted sugar better known as caramel. But as I said here it seems to be written in 2 words. So chou as an adjective is the exact meaning of cute and as a noun (except from cabbage) it means my dear or my love you can say ’mon chou’ to you children or your partner for instance. So the perfumery name can be translated in many way some more funny (my cute cabbage) and some more romantic (my cute love) it’s up to you to translate it how you prefer ^^
I'm French too, and it's quite obvious that a perfumery name doesn't refers to a vegetable or an elastic, the fact that it is written in 2 words could be a mistake or pun. I currently leave in germany and I saw many shops named in French with error in it so I wouldn't be surprised. The chou for a child or partner combined to cabbage sounds really "tiré par les cheveux" and unlikely, but anyone can imagine what they want ╮( ̄▽ ̄)╭
Haha in French when someone says "mon chouchou" it absolutely doesn't mean "my cabbage", in means "my favourite person". Cabbage is "choux".