Maybe the same white as the trim in an eggshell finish

I dont think, it is the walls. I think its the brownish color of the furniture that is clashing with the floors and the wall colors.

Your furniture is not arranged correctly for this room. I don't have any dimensions but I know that the sofa should not be placed directly in front of the fireplace.

Try this layout and see if this doesn't work better for the the furnishings you currently have.

A gray and blue patterned rug will help link the furnishings to the paint color on your walls.

If you break up your walls with large canvases, the room will not be so dark.

This would have taken less than the hour it took to do this if the photos hadn't been so very wonky.

The deep gray/blue walls are light-sucking. Whatever color the trim is - have it mixed one or two shades darker for the walls.

The fireplace looks nice. Why is the furniture in front of it? Your rug looks too small.