Please draw a sketch of how you want the doors to look when finished.

Do you want the top to be an arch or an arch within a rectangular frame?

Include measurements.

You'd get some relatively thin plywood, cut the pieces to fit inside the rectangles of your doors, then cut the arched empty spots (this requires some skill with a band saw). Then, you sandwich linen between the two thin pieces of plywood, glue them together and install.