I just had my living drapes installed yesterday. I have a huge window as it runs the length of the living room including the slide out door to the balcony.

I also have shades which are what I use to cut the glare from the eastern harsh sunlight in the morning. That is the only time I have the shades down and I obviously don't need drapes for anything other than to soften the visuals and add visual interest.

Mine are just tie backs at either side of my large expanse of windows and I love it. I don't regret it because it would be stupid for me to have excess drapery fabric that was never used. If I actually needed it, I would have done it but god knows the cost of my drapes was a few thousand dollars anyway because I fell in love with a fairly pricey fabric and fabrication is not inexpensive either :-).

I love the finished visuals as it accomplishes exactly what it was intended to do which is provide visual interest and softness.

Drapes will add a lot to the room and do not have to be functional to look great. Use a nice rod and place the rod half way between the top of the window and the ceiling, or what is closest to getting your drapes to the floor. Mount the rod brackets a bit outside the window itself (3 inches or so) to visually widen it. Homegoods/TJMaxx etc often have some nice cotton/linen drapes that look great. Try to stay away from polyester as they tend to look cheap.

Is that a chair rail or a larger ledge just beneath the window?

If the sofa is to be set with its back to the window, you still should seriously consider adding curtains drapes over your shade but use wider/shorter curtains/drapes rather than a floor length window treatment.

Using a double rod hung as high as possible and at least a foot wider than the single window, you could use a really good long swag ( always open ) over white sheers ( always left closed ), with the sides of the long swag covering the sides of the window frame and some of the wall beside the window while leaving as much glass visible as possible. Doing that would visually enlarge your single window.

Window Toppers sells different lengths of swags, lined and unlined, in various colors. The off white/pale tan would look good with your yellow sofa and almost anything else.

https://www.swagsgalore.com/emmett-3pc-lined-63-swag-set-sand.html

If possible, center the sofa in front of the widow rather than off set.

Your drapes need to stack back on the wall beside the window. Even if they're stationary, they should still look like functional drapes with the same stack back. Will you be moving the cabinet that is to the right of the widow? Because right now you have no wall space beside the window for drapes to hang. https://blog.drapestyle.com/curtains-drapery-shades/what-is-stack-back

What the heck are board mounted drapes? Anyways, side panels would look great on this window. The thing about stationary drapes is they shouldn't look like stationary drapes. So often you see large windows with skinny side panels and it looks terrible. No matter what the fabric, the rod or even what the rest of the room looks like, it looks cheap. So, don't skimp out on the amount of fabric which is what you mentioned you wanted to save money on. Hang your rod half way between the top of your window and your crown moulding so your panels are a long as possible. This is to accentuate the height of the room (panels that are too short make the room look squat). Minimally, each side panel when fully extended should cover the window so that your fabric amount is double fullness. When choosing the size of rod, allow for the width of your side panels so they aren't covering a lot of your window. The goal is to make the window look bigger than it actually is. Here's a trick for stationary panels. Often it's hard to keep panels in place on the rod and they start to creep closed. This can make one side of drapery more open than the other and the whole look is lobsided. Here's the tip, put an elastic band on the rod beside each panel and arrange your panel so you can't see it. Your panel will stay in place.

Stationary panels would frame them nicely!

Since you have a roller shade already, adding some fabric in a whimsy pattern could be FUN!

What the heck are board mounted drapes?

They're curtains mounted on a 1x2 or a 1x4. Used for stationary curtains and to save money on not having to buy a rod or because a rod is not wanted.

Will look like the ones in the pic that Gordon posted.

Ikea has nice draperies.

Depending on your budget, you could either buy them ready made or have them custom made. I just put up ready made pinch-pleat sheers on an expanse of 4-36" French doors. It's for my vacation home, so I didn't want to spend a lot of $$ on custom treatments. They come with drapery hooks and I mounted them on wooden rod and rings. I bought them from the Vermont Country Store, and they are 144" wide. They look great and actually are polyester, so they won't wrinkle like the linen panels I had before. I love sheer panels, as they filter light but don't block the views!