How about something like this. I would put a sofa where the loveseat and chair are now, remove the two oak cabinets and put a narrow console behind sofa to put a couple of lamps on. Then put a loveseat where sofa is now, then put two chairs, one on each side of FP. Don't pick furniture all from one set, it looks better to mix it up.
I agree it's a beautiful FP, and although you didn't ask I have to add I really don't think the style of the columns belong there.

Thank you for your ideas. Good point about the columns. What to do you think about an area rug. Would that even work because of the doorway?

I agree about the columns -- I wonder if it is practical/structurally okay to box them in? I'd also recommend just for starters an updated colour for the room, although what exactly it should be would depend on your eventual choice of upholstery, rug, etc. I love the clean lines of your lamps and would use them as a starting point for the style of any wood furniture you buy. The upholstered furniture could be streamlined too, but I think it might be more interesting to have round, comfy shapes. There is so much for you to decide, but what fun. I've moved a new coffee table in below, just as an example of something handsome that echoes the limes of the lampshades.

As far as a rug is concerned, it looks as though you could use one in what is now the area between the sofa and the TV -- that side of the room, and leave a clear passage from the study door to the kitchen/dining area.

This room looks fantastic! If you get inspired to try something new when rearranging, then why not try a wall art sticker? The colour scheme employed by the room as it is now would go perfectly with the kinds of wall designs we can provide you! You can take a look at them yourself on our website at:
http://www.infinitywallart.com/wallstickers

If you did the furniture arrangement I suggested, it might look odd to have a rug just on one side of the room, and not go to the sofa. I think you could do one large area rug or a piece of bound carpet, but you would be hiding your lovely floors. If you wanted an area rug just on the FP/TV side, then instead of a sofa on the doorway side of room, set it up so it's like a separate area, reading nook or something. Maybe a lounge chair with a small table, floor lamp and bookcase.