eply to Andrew's comment below. There's nowt like a bit of english telly to encourage them along (and you, whilst filing your nails, can watch BBC4 documentaries which my kids now watch - when they are not plugged in electronically !)
Otherwise our librarian here encouraged the kids to take out bandes dessinées because that gives them exposure to current spoken language. Not many though in english. They will learn it when they become the go to person in college english lessons or when they perceive english to be cool - like you say no point being too hung up about it.
Sadly now my children speak more english than french since OH is here more often. One even did his Bac TPE in english with his friends who are in an english euro SI class. So I feel the same as you in the opposite direction.
Even more annoying is their lack of ability to learn spanish in the classroom because they say they don't just want to learn vocab and conjugaison