Adjust both doors to ensure they are properly aligned with the door frame. Over time, doors can sag on the hinges, causing gaps that let outside air in. Tighten the screws in the hinges to pull the doors back into place. In drastic cases, reset the hinges as needed using a drill to remove and replace them.
Install adhesive weatherstripping foam around the door frame where the French doors touch the frame. Remove old, torn, gaping weatherstripping foam. Clean the door frame with all-purpose cleaner and a rag. Cut weatherstripping foam to the length of the sides and top of the door frame, then peel off the adhesive backing. Press the weatherstripping foam into place one strip at a time. Rub your fingers up and down over the weatherstripping foam to eliminate air bubbles. Open and close the doors a few times to ensure there are no gaps between the door and the frame.
Check the seams of the French doors for cracks. Look for cracks in the area around the glass, because the seal between the wood and the glass can wear down over the years. Fill cracks with caulking, and allow it to dry completely.
Close the gap between the two doors with insulated molding. Nail it to one of the doors using small wood nails so that it overlaps the other door by about one-half inch, covering the gap. Place nails about every 5 inches. Cover the nail heads with wood putty and sand them smooth. Paint the entire French door set, including the insulated molding, for a professional, finished look.
Install door sweeps on the bottom of the French doors. Remove one door from the hinges and set it upon two sawhorses. Use a drill to affix the sweep so that the blade edge is on the inside of the door and the drip or tube edge is outside. Repeat with the second door. Rehang the doors so they align properly and the door sweep creates a tight seal between the doors and the floor.