Considering the often tight connection in CDG you are better off staying overnight in a cheap airport hotel.
If I was booked on a through ticket, I wouldn't worry.
Stops for me are usually a bonus - I already have a very long list of places in & around Paris I haven't seen yet. As an architect, that STARTS with the CDG terminal. So you are right - except I'll probably do two nights and stay in centre of Paris.
Flight departs 11:40 - no way I'd try and do that on a separate ticket BHX-CDG as a feeder, and even though that would still be with AF/BE anyway, the days of two tickets being joined & bags checked through are long gone.