A rug won't solve the problem all by itself. Since the couch was "free," consider reconfiguring it with fewer pieces. You would have a much airier space if you eliminate a whole side of the sofa so that the dining area can connect--either two facing sofas or sectional plus a chair or two would making the room much more inviting. Pease take a photo of the opposite wall? You haven't given us enough visual information. Is TV watching going to be part of the room?
Here are some general principles when dealing with oversized, heavy, dark pieces
--As Partim said, add pattern and color to curtains, rugs, wall paint, pillows, and accent pieces like coffee table and side chairs.
--Contrast the finish of the main pieces, i.e. the massive leather couch, with different materials that have a smidge of the color--black/brown--but it 90% some other color and/or pattern. Can't tell if the couch is brown or black.
--Add art to pull the eye away from the sofa. The art could be in the dining room.
--Add ambient lighting--floor and table lamps--to bring light into the room. Get modern, industrial looking spindly lamps. (I know you're looking for a farmouse/lakehouse vibe, but the couch isn't either of those things. Sorry, but it's a bit fraternity house, a bit rec room, which is why I suggest breaking it up into two sofas, or one sectional, not a wall-to-wall barrier to the rest of your house.)
--Coffee tables, consoles, side tables, etc. need to be open and airy. That doesn't mean delicate but up on legs. Since the couch is leather rustic wood pieces will work but with open legs. Curtains should be nubby with maybe some bamboo roman shades. Or just the roman shades. See photos below.
--You'll have a more inviting, flexible space if you rehome half of that couch and add a couple side chairs. Otherwise, you'll have guests lined up along that walls with vast space in between--not cozy. And getting to the dining room easily looks almost impossible. The couch blocks the flow of the space.
Because the big leather couch problem comes up repeatedly on Houzz, I started an Ideabook called Brown Black Leather Couch Dilemmas to see how to deal with them. If you click on my name, then look for that Ideabook, you can see how pattern and colors are used in different rooms. Some of the rooms just have simple shades to let in maximum light.
Again, a rug won't fix the problem of having a massive sofa dictating the feeling of the room. Try splitting it up if that can be done. Many of us would like to see how that looks, so come back with more photos, particularly the wall that isn't shown.
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