I had brand new pre-primed unpainted french doors installed and now I have to paint them (also need to paint the new door frame). I plan to remove the doors from the door frame as well as remove the door knob but is it best practice to also remove the hinges from the door and frame before painting? My concern is it not screwing back in cleanly once Im ready to put the hinges back on.
Removing hinges can very definitely lead to fit problems later. Also, it's not easy at all to balance a door while trying to screw hinges back in -- especially heavy doors, which French doors are bound to be. Do not remove them from the door. Put masking on the hinges (don't leave tape on longer than necessary) to protect them from paint -- nothing looks worse than hinges gopped with paint.
If they are split pin hinges, remove the pins, leave the hinge leaves attached to door and frame. Mark the pins so you can put them back in the same hinges.