Double doors are inherent leakers. I would never use a double door without a significant overhang for protection. The picture does not blow up at all to tell wheat your current door is. However it happens I would lose the arch and again with a single door with 2 sidelites.

I removed my double door and installed one single door with two side windows, allowing great airflow. I also carried the stonework around the window to match the outside stone walls.

Beautiful home and it does not need much. The Ivory trim feels tired to me and does not tiie the brick and roof together, so I would paint all the trim and wood a grayed white or a pale neutral gray.

Here is a very rough sketch, no fancy software, just to try and visualize.

I added a single door in Sage with sidelights as suggested and I would listen to millworkman.

Gray

Or some type of color like Taupe or Sage