I would love to find out where you purchase the bright-red tree print fabric. Thanks

I dont think the window or door is the issue here. Its the fact that it is such a very dark room which makes it ugly. Get the lighting sorted first, then I would put sheers up to let in the maximum light.

It's actually pretty bright, and the window and door frames are blue grey...

If you don't plan on opening the window, you could stretch white or cream sheers between 2 spring rods (one top, one bottom) set inside the window box. Then hang draperies on a heavy rod (those frames are "massive" so you can't go dinky) with draperies that go from the door to the wall. Something with grommets will make it easy to open and close and look modern. Assuming modern is your style.

I rather like the architecture and windows for their somewhat Oriental vibe because all the trim is such a stark contrast to the walls.

I'm actually planning on painting all the trim white. I'm going for modern, contemporary

Oh perhaps its just the photo. Yes painting them white will certainly be an improvement then.