I"m not a big fan of fake windows, either.

What I'd do is create a balance between the sides of the room using other decorating techniques.

For example, if you can find a piece of artwork that's roughly the same size as the window, you can hang it in approximately the same location on the other side of the sofa. But given that these windows tend to be rather high on the wall, that might not give you the look you want in the room.

But you could also put a small bookcase with a lamp on top of it under the window. Then put a similar, but taller bookcase on the other side of the sofa. The two sides won't be identical, but they will balance out.

Or create a vignette under the window with a table and lamp and vase and flowers. Then on the other side, have a similar vignette, with artwork above it.

The two sides of the wall don't have to be identical to be balanced.

Have you thought about running drapes the entire width of the area you are trying to get symetrical including behind the sofa?

I have the same window in our finished basement which I am tackling now with full length drapes. Ours opens for air.

Could you post a picture?