Just 8' width?
Considering the inward slope of of the roof line, your going to be grossly limited in two things.
Screen width and height of placement.
Also, unless you plan to make a Frame that will completely cover the window, there is not chance the Screen itself will do so.
Lastly, it's a good thing you plane to do something with those white Ceiling Panels because no matter what, the top corners of any size screen chosen will be almost right up against those surfaces. So reflections off them will be intense. I suggest instead of Cloth that you consider a very Dark Slate Gray in a Flat sheen. Gray and Blue look great together, and a very dark Gray actually suppresses light reflections better than a Black-anything excepting Black Velvet and ProtoStar Telescope Flocking.
Logistically, the small size of your room, as well as the sectional seating, both combine to make you have limited choices. One good thing.....the 1600's Image Offset now works to your advantage since the bottom of any screen will be fairly low on the wall. By my "eyeball" judgement, the bottom of almost any size screen worthy of note will be at least on the same level as the arm of the Sectional seen in your image.
To determine you largest screen size, start with these measurements: 63" wide -- See just how high up on the screen / window wall you can squeeze that width and still leave at least 2" at each upper corner. Then measure down 35" and see how far off the Floor that will be.
Obviously....an alternative measurement is to simply go up to as high as possible that gives you any width greater than the aforementioned.
Do all that, then come back with the tale of the tape....be it grim or still potentially do-able.
Miss St. rules. Naturally.