Beautiful floors -- would not cover them with a rug.

I note the placement of an overhead light fixture that (I'm guessing) may be one of four in the living area -- two on one side and two on the other? If this s accurate, Have you considered turning your couch and adding either a sofa table or a bookcase behind it so that creates a hallway behind it? You could put a runner rug to protect your floors and define this hallway and let the beauty of your living room floors show

From what I see, your light fixture(s) would likely put light over the sofa if you need it so you wouldn't necessarily need lamps on end tables beside the sofa -- at least not on both ends.

Your chairs would go across from it and, if that is the direction of either the kitchen and/or hearth area, the traffic to those areas could pass between them.

Either that or I'd seriously consider moving the sofa to the window area instead of the two chairs.