I have an old house too-I understand! I wouldn't cut your drapes and would suggest light fabrics that fall to the floor. If possible move the sofa away from the window a bit but dont cut the drapes!

Have you considered layering your window treatments? We have roman shades on our windows for privacy and for a cohesive look from the street (different treatments visible from the street alter curb appeal). They also let light in when drawn. We also framed the windows in a light fabric drapes to suit each room. This allows us to admire our old windows without them being naked and gives us the privacy when we want it without losing the natural light.

Hope my rambling helped!