It will be attached to each side of the window so as not to fall...

Is the mural like a natural scene that should look like it would have three-dimensional depth to it like a forest scene that goes to mountains? If so, why would you need it to curve away? The depth inherent in the image should provide that because it seems to me it would be more natural in appearance, that is, more like it would look as if it was a real scene.

If not, and you mean something else, I suggest you consider using a professional to create that for a high-quality look. Unless you have the skills and knowledge to pull it off this might not work.

Having said that, I might check art supplies stores both in person and online. They would probably have ideas. Maybe a custom frame shop could suggest items as well.

I would use wall board. That might not be what it is called. I am thinking of the stuff that is sold in 4'x8' pieces at HD and cost about $20. Lots of people use it to make dry erase boards. Sometimes people buy it to make a skating rink for their kids. You can slide on it really easily when wearing socks.

ETA:

I found it. This is what I would use.

Plastic Wall Panel

Thank you very much, I will go to HD and check that out.