How to repair bowed sliding door frame?
From you post it appears that the French doors are OK but the problem is with the sliding screen door.  I'd get a 6.5' 2x4  and my car jack and try to lift up at the middle of the frame to see if it's just separated from the header or if you have a structural problem. If it can be lifted into position, refasten it with some long wood screws through the frame and into the header. If it can't be lifted then you have a more serious problem and you'll have to remove some siding to investigate further and report back here.