I guess you need to define your style goals. The built-ins give the room a bit of an ornate/formal look. If you want something different, you're going to need to address more than furniture.

I think the chandelier is pretty but I don’t like the shades. Have you tried taking them off to see how it looks?

The chandelier will never go with a farmhouse table! It sounds like you already know that. By built ins, are you talking about the fireplace? If those are doors, just order new doors and have the entire thing professionally repainted. I would go with a simple Shaker style door.

I don't see any farmhouse elements in your photos. None of the accessories shown says farmhouse either.

Pictures of all the walls in the room will help....but from what I see removing doors to open shelves might give more expanse, and a new chandelier; buy the table and chairs first then decide on chandelier last.

I would remove the built-ins, the narrow hearth, and the mirror over the fireplace. I’d redo the fireplace with brick or stone, with a wooden mantle. A lantern style pendant, or two, depending on the length of the table, to replace the current chandelier.

I really like the cabinet doors surrounding the fireplace. I think the mirrors are and will magnify any lighting that you choose, and not in a good way. IMO get new curtains, take down the mirrors, then decide on the lighting. Sorry, I’m getting ready for work so no time to find suggestions for you. I love your dining room. With a few tweaks it will be gorgeous.

Is the rest of the house as traditional/formal as the dining room? If, so, you have a long road to travel before you have success in turning your home into a casual country farmhouse.
If the dining room is the only traditional/formal room, you will need to remove all the mirror, the ornate doors, all the heavy moldings, the cornice on the window, and the formal chandelier. The fireplace can be reworked, too.
Do you have a photo of what you envision for your room? We will be able to offer more suggestions if you will add a photo or two of your inspiration dining room.

I agree that the ideal is to redesign the wall totally (and not only because it really doesn't chime with a farmhouse feel; it's just not a great piece of design). But if you don't have the budget for that now then replacing the ornate doors with simple ones will help. Also, removing the mirror. I would consider painting that massive white step to match the floor, too. Start saving for a great revamp.

I think we need to see the rest of the room to gauge scale and shape for a chandelier. Do sell the one that is there -- it's too pretty not to go off and make someone else happy. Is this room open to the living room or kitchen? What style of lighting do they have?

A farmhouse look will require a pretty hefty change to your formal dining room. Remove mirrors; window treatments; chandelier; and built-in doors. Replace mirrors with open shelves; window treatments with a grommet top linen on an iron or wood dowel rod. Replace the existing chandelier, which is really beautiful, with iron or wood or maybe a few pendants. The built-in doors could be replaced with a very simple, natural wood to complement the floors. Add a needlepoint rug and your farmhouse dining table and chairs. Paint the woodwork tan and walls ivory.

Keep the chandelier and remove the shades. You can get a farmhouse feel while keeping the more formal bones of the room in place.

Fireplace wall: paint the floor molding on the hearth, the cabinets and the walls on either side of the mirror black…(.black cabs/black fireplace). Leave the mantel (gorgeous) and the frame around the mirror white. Hang a mirror over top of the mirror. This one, made of bark, might complete the look.

This room for inspiration:

I love the fire place and moulding.
I would remove the glass shelves and mirror.
I would also remove the blinds and drapes and the shades on the chandelier.
This will immediately change the look and give you a better perspective.
I think the picture below gives you an excellent idea of how to bring it all together.
Are you positive you want a farmhouse look or do you want the longer table? There are lots of tables to choose from.
Is the rest of your house farmhouse in style?
The fireplace area could be very cool painted a high gloss black still removing the mirror and shelving and window treatments.
The look could lend itself to a more traditional or transitional look which I'm guessing the rest of the house is more of that style.
You need to stick with one style throughout your house but could get away with your kitchen lending itself to more of a farmhouse theme.
Best of luck!!

Here are some gorgeous chandelier ideas from some of our designs that might interest you.

Is anyone else seeing Art Deco in this space? That FP wall is practically begging for it