Measure the height of your double doors at the point where they meet in the center.
Cut two strips of 1/2-by-2-inch wood to the length you measured in Step 1.
Apply one strip to the interior side of one of the doors, positioning it so that it spans the gap between the two doors and overlaps the edge of the opposite door. Attach the strip to the door by driving in a 1-inch-long screw every 12 vertical inches.
Place the other strip on the exterior edge of the other door, screwing it on so it spans the gap between the two doors on the exterior. You now have both an interior and an exterior strip covering up the gap between the doors and allowing for future expansion and contraction.