Im not sure you can do anything there, any curtain would would be a severe fire hazard.

For privacy, use window film cut to just fit inside the decorative edging or an inch narrower on all sides.

A top-down blind?

Thanks for the comments. We only need privacy at nighttime - we would want open during the day.

Very odd layout with those two tall cabinets.

Hmm. I wouldn't put anything there. The windows themselves are beautiful. Agree that window film that allows you to see out, but not in from the outside, is the best solution.

For you style of windows I would recommend a solar shades. When I have wanted an inside mount for shallow windows I typically have a trim piece added to the existing trim and mount the shade to that. You have a beautiful window and trim so it would be a shame to cover that up. Mount two small shades underneath the mullion so the top portion of the window is still exposed.

I wouldn't have ANY type of material hanging that close to the range. Yikes. Window film is the answer.

This is a very confusing kitchen when one thinks simply of function. I could not stand the counters being used up by those two tall cabinets. Your window dressing issue would be helped too if the one on the left wasn't there. This is twice now I've seen these cupboard stacks against the counter--a two centuries ago idea. I thought we figured out that is a huge waste of counter space????? That 6 burner stove and massive hood suggests some serious cooking going on. Counter space will be needed! Removing the cupboards will help with the cohesive look of your space too. Right now they look like preserved artifacts from the 'before' kitchen.

Your kitchen is beautiful.

I think you might have enough room for an inside mount Roman blind or cafe curtains on tension rods (I have cafe curtains and the rods are very small):

For either one, I’d mount them just under the middle trim.

You could also mount a rod directly on the trim, something like these:

Cafes mounted on trim:

Here you can see they used a return rod (or French return rod) directly on the trim … good for tight spaces:

Just research for inspiration pictures, I think you have plenty of options.

If you’d prefer some type of blinds over curtains, it might be worth having an in-house consultation with a local pro.

I would have an appointment with a professional window design company. They may be able to figure out an inside mount. I agree that you need to be careful with “billowing” fabric near a range.

Select Blinds has several “no drill” window treatment options. You may be able to get two separate ones to fit inside the frames. Best wishes! https://www.selectblinds.com/no-drill-blinds.html