What I would do is put either a sofa facing the fireplace or your two recliners facing the fireplace with a table and lamp between and then in the space between the two french doors, I would put a small round dining type table -- 30 in to 36 inch size and 2 to 4 chairs.. You can perhaps put something against the wall -- that bookcase, a sofa/console table, etc. You can use "outdoor/wicker" type furniture or inside furniture IMO or a mix of the two.

I have a long, narrow sunroom in my 1939 house. I put a daybed at one end and it's my favorite place (my dog agrees) to hang out on a sunny day to read, nap or use my notebook computer. It sounds as though you'll use yours like a family room since you list a TV. Then, I agree with Martha Scott and divide yours into a seating area with the fireplace as the focal point, then use the other area for a dining nook.

It's true in the winter the sun comes in and warms up the room it's very very bright.

Try a couch against the bottom left wall with 2 chairs opposite it, in front of the windows with a small side table between them. If the chairs swivel, then you can turn to face the view, the fire, the couch for conversation, or the table area.

It looks like you should have room for a small table and chairs in the middle of the right hand side of the room without interfering too much with the walkways.