https://www.lifeofanarchitect.com/residential-architecture-101-shutters/

Shutters as they are aren't doing your home any favors. I suspect landscaping might give the needed boost.

You'll need to make the widow smaller if you really want shtters up there.

The issue with the windows isn't the lack of shutters on the arched window, it's the presence improperly sized and obviously fake shutters on the downstairs windows, along with the disproportionately skinny trim on the downstairs windows.

My advice would be to remove the shutters on the downstairs windows and replace the awkwardly skinny trim with some new trim that is the same thickness as the arched window with a nice header piece (similar to current header, just bigger).

I don't think your house ever had shutters. The trim around the lower windows on the sides is very narrow, it wouldn't support hinges. At any rate, shutters should be mounted on the trim, not next to it and be able to cover the glass portion of the window.

I actually think shutter for the half moon window would fit. If you took a piece of brown paper and fitted it to the window on the inside, drew the outline, took the paper down, cut the shape, folded it half, you would end up with the right size shutter pattern. Then the shutter could be mounted on the window trim, right next to the window. (Because the photo was taken at an angle, it looks like it does fit on the right side, but I think the left side shows that it could.)

I wouldn't put shutters on your house.

Cute house. No shutters on upper window. Please get someone who can properly size and install the lower ones. They should be only as tall as the actual window itself, should be wide enough to cover the window when closed, and should attach to the window casing, not the wall.

https://www.thisoldhouse.com/how-to/how-to-hang-exterior-shutters