Some internal French doors are built with a strip in the centre of the door frame that sits between the two doors. This is called an ‘astragal’.
Astragals are usually made to have the latch plate fitted to them. So that when you have one door open, the other is held firmly in place. Alternatively, the latch plate would be fixed to the second (slave) door - this means when one door is open, the other could also be opened easily.
Not all French doors have astragals as they obstruct the doorway. They can be seen as breaking the flow that French doors are supposed to provide between rooms.