Duplicate the base image and work on a copy that will be masked into the original. Image > Adjustments > Shadow/Highlights and bring up the highlight value to attempt to rescue some facial detail. Further work will of course be required to even out tones, however the all important facial detail is critical to recover.
I added a black and white adjustment and focussed on matching the grayscale in the light rectangle as best I could to the area outside the rectangle.
I then duplicated the original and set it to blend mode color - and brushed colour from the bottom of the picture into the rectangle.
Finally a little cloning to remove the edge.
Far from perfect but it may give you some ideas
One adjustment that is often overlooked is Image > Adjustments > Shadows/Highlights. It does not have its' own Adjustment layer, so the changes are permanent or "destructive". Still it does a nice job. I eyeballed this one moving the colors away from the Highlights and towards the Shadows/Midtones, but there is that streak across the image.
It's a "quick and dirty" adjustment on a laptop screen, so those of you with better displays can see what you can do.
gener7 & Dave, thanks for tips.
Dave I see that you did a curve adjustment too, can tell me what part of the image you used it on? I'm still playing around trying to come up with what both of you did - been awhile since I done any photo restoration - will have to get the cobwebs swept away.
I used the contrast layer to try and match the grayscale of the faded rectangle with the none faded section. Although it was one curve I used a soft brush on the mask so that it affected areas differently. Don't be fooled by the white on the edge of the mask. The layer was also clipped to the layer below so the good areas were not affected.
This greyscale match was done before reintroducing colour with the top layer.