How can I make a fireplace cover more farmhouse-style (pic)?

Maybe paint them a contrasting color? Black could look modern and farmhouse.

Stencil the edges or the shutters themselves!

I vote to finding a fun actual fireplace screen the correct size.

I would use 3 shades of a farmhouse blue to give it dimension. Maybe add a light inside the fireplace to give it a new dimension at night.

Then I would add a much larger topiary on both side, or maybe some large tole ware pieces to pick up the framhouse blue.

Also, from what I've seen on this site, 'farm house' style means flat trim, not like what your trim is. So, you could replace them or fill to make flat and paint.

I gotta agree with Kelli. Fire prevention and Safety is a Priority. You do not want those shutters ablaze in the home.

You have the bones. Make the shutters into a screen.

https://www.hometalk.com/diy/living-room/fireplaces-mantels/farmhouse-fireplace-surround-makeover-on-a-budget-27671102

https://www.hometalk.com/diy/living-room/fireplaces-mantels/farmhouse-chic-fireplace-makeover-28308545

Screen

https://www.hometalk.com/diy/living-room/fireplaces-mantels/fun-and-easy-fireplace-screen-10037591

https://www.hometalk.com/diy/living-room/fireplaces-mantels/diy-picket-fence-fireplace-cover-15046969

I think that the 'screen' looks lacklustre because:

-it is flat. It needs to be slightly bent to give it dimension.

-the portions that have been added above and below the shutters are not a complementary size or the right scale. They made the unit look like some kind of flat wall art (? )rather than a fireplace screen

-it lacks color and pattern