How to hang curtains on old window frame?

How about a branch or tree limb?

You could staple the curtain fabric on the back side of a fence slat. You might want to "rough up" the slat first if you are going for a farmhouse look. Best of luck to you.

Choose cabinet door handles that match your decor colors and intertwine loose fabric instead of curtains

Attach shaker pegs to a strip of wood that will be above the window. Hang tied curtains (with the pairs of strips knotted, not tied with a bow) from the pegs. Tied curtains have two strips of cloth,in pairs that emerge along the curtain top, perpendicular to the top of the curtain, if that makes it clearer...

I envy your 4-pane window. The coolest thing I ever saw was a window like that hung on a wall and behind it was a poster of a large field of flowers. When you looked at it, it seemed like you were looking outside. I have always wanted to do that but YOU have the window. You could put a field of grazing cows - talk about farmhouse! I'm Jealous.

I'd get shutters for each side.