The screw through the head is factory, I have had lots of Bayards and I have never seen one (that I can remember) without the screw.
This is a unusual action for a Bayard and only the second of this type I have seen (the first was a much plainer gun). Most Bayards have a crossbolt and rib extension. Notice this gun does not have a screw for the opening lever and when you open the lever it cams back a small piece from the top of the rib. Also the action is more "square" than most Bayard models. Interesting gun.