Yes to a thin frame, and line it up no higher than the door frames' height or lower. I'm 6 feet tall, and if you hang it as marked with the tape, my eyes will be at the level of the bottom 1/3 of the painting. That's waaaay too high.

That's a standard 6-panel, 6-foot 8-inch door, and my eyes are right at the bottom of the top two panels. The center of the piece should be below that for me, and most people are shorter than me.

If that wall fireplace can't be removed, then don't put that painting there. But what a goofy place for that fireplace.