French doors, or commonly called double doors, rely heavily on one of the doors being able to act as the wall and the door frame at the same time. To do this they will always have bolts on the top and the bottom of one of the doors to keep it secured and unable to open. Then the other door latches and locks the that door. Confused yet? Well don't be, just trust me that if the stationary door is wiggling at the top or the bottom, the doors aren't truly locked.
The bolts that go into the frame above, and into the floor, or Saddle/threshold on bottom must be working properly and going through a strike plate with long screws just like any other strike plate.