I think a fan on the beam will look out if place. If you have your heart set on a fan, I would install two plain white fans, equally spaced next to and along the non-fireplace length of the beam and so the blades don't overlap the beam and each is 1/3 into the room from the sides. Make sense? The idea is to make them as inconspicuous as possible but to get the use of the air movement throughout the room.

Agree with not putting fan on beam. Due to ceiling construction, a problem with running new wires. Why not use the ceiling light to Right of beam, 2nd from window wall (if that makes location fairly central)? Drop fan to below beam. With the MC open-beam style, would go for fairly sleek, modern design, on remote switch. And for that style reason, don't care for the rustic fireplace insert. Could replace with more modern one, wood, gas, or electric depending upon availability in your location.

Thank you for your thoughts.