Are swag type curtains out of style?

Roman shades

Yes. They're currently out of fashion. Take the wood blinds down and switch them to the insulating honeycomb type blinds. If you're in a store with a large magazine selection, look at current issues of "house beautiful" for some current style information.

Swags are very much out of style! Wood blinds in white are in style currently. You can leave as is or put up extremely long sheers at the sides, etc.

Well so far 2 opposite answers, which leaves me to ask you what is your style? It's a formal living room, how formal,the kind no one enters? Leave blinds those never go out of style. As for swags if you are getting these made and you personally like them what I would add to bring up to date is a one panel drape at either side of bay window. These finish the swag off and make sure you hang everything much higher then we use to they need to be at least four inches above window frame so swag needs to hang long enough to cover window frame. Then do the same on the other windows. These don't serve any purpose but to add a finished look. I wouldn't add fringe or anything and of course these panels just hang they also need to extend at least four inches beyond the window frame. Try to stick with solids because in my personal opinion having these made cost to much to have to stick with a pattern for several years. If these blinds were anywhere else in your home I would say no curtains just blinds. These are like subway tile they will never go out of style have been around since plantation'so that's why they are often called plantain shutters or blinds.

Houzz.com and architechturaldigest.com are great sites for inspiration and design lust.