1. Whilst you can book via air france or flybe, any MAN CDG/CDG MAN sector included under the code share agreement, the operating airline could be the opposite. Whilst you booked via Flybe.com, the flight was operated by AF. At MAN AF are not handled by Flybe/Flight support. They are handled by swissport. As such they have seperate checking staff and desks, albeit located right next to each other.
2. I have no idea. Bad luck perhaps?
3. The vast majority of AF pax are connecting around the world. It takes longer to check them in, especially is one of the sectors is delayed as this will have a knock on to the transfer. If you happen to be checking in whilst passengers travelling to certain African destinations are at the desks.......expect a long wait. It happens all the time at the AF/BA/BE/SN desks. Apparently they never knew a baggage allowance existed, and that engine blocks for Toyota pick ups need to be sent as freight. Oh happy days.