There are a variety of arched French doors.

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You could make it an arched transom window, which would bring more light into the entry. Or you could leave it as is and paint it to blend into the stone and disappear.

I don't mind the arch(s)

I would paint them the same color as the door. including the sidelights. whatever color you choose.

as far as the window, I would paint the arch the same color as the shutters.

Thanks for the help. The other side of that door arch is attic, otherwise I’d absolutely go for an arched door or transom window!
I think the “fan” texture is what really ages it, but don’t know what else it could be.

The arch will be with you until you move.

Could you make it a frosted glass arch?

I'd change the light fixture sooner than I'd change the fan arch

I'd add a really large mat in front of the door and put wider, actually functional shutters on the arched window.

Have you got a color scheme in mind for the door?

Replacing the leaded glass with plain glass in the sidelights will make a huge impact. As for the arch over the front door, reeding and fluting is on trend, but you could replace that piece with a plain piece of painted wood (I like it the way it is).

As you yourself have noted, it is the fan design that is bothering you more than the arch itself. Plain wood will fix that.

Personally I think the leading of the sidelights ages the house more than the fan arch. Get a new door and sidelights in a new color then see if you still are bothered by the fan arch. It looks like a beautiful house from what I can see in these two pictures.

Paint the arch a color close to the srtone and IMO take the shutters of those windows with the fan above just too much going on there .IMO the door and sidelights are one piece and should be the same color .

Can I ask if you ended up changing them? I have these above windows on my house and I really dislike them...

No changes, I haven’t found a solution that I like yet.