Not a designer. How about a rug that is primarily beige/tan with touches of some jewel tones (ruby, sapphire, emerald, etc) and then introduce some of those jewel tones in artwork, pillows etc??

The red with your wood is fine however the blond wood on the chair and ottoman is not. I would stain them dark or darker to blend in. Very nice room and beautiful floors,would be a shame to cover them up with a rug but I know most people would suggest doing just that.

Your metal piece over the FP is very mid century and goes OK but if it were my house I would get an abstract painting instead.

@gustaruygers I totally agree. We bought the armchair this weekend and my next project is to stain those legs.
The mid century modern piece on top of the fireplace got there in a bit of a funny way.
As I mentioned, this is a rental, and lots of things about it are very, very dated. The fireplace had a horrendous, thick brass frame around it. We tried at least 4 different paintings on top of it, and nothing could compete with that monstrosity.
So I decided that if you can't beat them, join them, and bought this brass piece to put on top of it.
That was the only way I could live with that thing.
Lo and behold, we were having dinner the other day looking at the fireplace and talking about how ugly it was. I got up and started messing with the frame, and realized the whole thing could come out without dama anythinf

So now we don't have to look at the brass fireplace anymore, but I haven't had a chance to find the right painting yet. We need to see what direction we go with the rug first.
Thanks for all your ideas!