Thanks for the advice. I ended up buying some miles

(there's a slight promo on at least...). They were indeed credited instantly.
After what MR said, and what people have said here, I didn't want to risk waiting five working days (I have an issue with the expiry of my FB miles, so didn't have time to wait..) for FB to credit the miles. True - I could have been a bit more organised on this, but FB award availability makes it hard to make bookings at all...
Still - at least I will now get to use a big chunk of FB miles, something that has become more and more difficult these last years (I too have fond memories of Fréquence Plus in the late '90s/early 2000s...).