IMO do drapes on both and if blackout is a must then do blackout drapes . or if you want to trearthem differently then drapes on the door s and a matching roman shde on the other . BTW unless you spend a lot of time in the bedroom during the day natural light is really not a huge issue IMO.

I think a drape would be pretty and I agree that you don’t want room darkening. We have French doors in our living room and have cellular shades on them. Definitely not as dressy as drapes. If you zoom in on the pictures you can see how the shades are attached to the door so they don’t bounce around when you open the door. I leave these shades open most of the time, but lower them on hot summer days. Today is a cloudy day so the light is darker than usual.

I’d keep it simple and depending on the privacy required, there are lots of options.

Something like this would look great