Obviously, the curtain is hung that way because the window is so high up near the ceiling. Not sure how you would run a pole. I'd leave it!

I'd love to see a close-up of what is up there.

@nhb22 The window is not so high up. The roman is placed right below the molding which makes the window appear bigger. I can move the Roman down as well as my curtain.
The curtain is held by a curtain track.

I would move them both down, the ceiling looks crowded the way they are hung. Maybe split the difference between the top of the window and the molding?

Agree to lowering the Roman and installing a drapery rod beneath the crown molding.