Check the hinges to see whether they have dropped. Use a screwdriver to tighten all the screws that hold the hinges to the door frame. This can lift the French doors up into proper alignment, allowing the doorknobs to move freely against the strike plates. It also aligns the doors so the door panels don't rest against each other.
Remove the doorknob trim by unscrewing the small screws on either side of the doorknob. Pull the cover plate and doorknob pieces out, then set it aside. Remove the bolt by unscrewing the two screws that hold it inside the door. Add it to the pile of hardware that is set aside in a safe place.
Take the door off the hinges by placing a flathead screwdriver underneath the head of one hinge pin, and tap the end with a hammer. Use leverage to pry the pin up, then work it free. Repeat with the lower hinge pin and catch the door as it falls forward. Do the same with the second French door if needed.
Examine the door for more clues on where it was sticking. Check the door panel edges for warped wood or excess paint build-up. You may need to plane some wood from the edge to make it fit better inside the frame. Other solutions include sealing raw wood edges with paint or sealant to prevent wood from swelling from moisture. The hinges may have been installed crookedly and need readjusted. Adjust the strike plate if it is not set properly on the opposite door. If the door continues to stick after all these solutions, contact the manufacturer or installer for repair information.