All of the answers are wrong. I recently went through this and hired a pro to fix it. For $1400 he shoved some weather stripping in my 4 sets of french doors. This is a garbage fix. Finally I fixed all 4 doors myself. What you need is a bump threshold. M-D Building Products 69709 1-Inch by 3-1/4-Inch by 73-1/8-Inch TH153 Bumper Threshold, Bronze https://www.amazon.com/dp/B003YUGSCC/ref=cm_sw_r_cp_apip_6VAqMTR5lSupb The bump threshold provides a solid aluminum bottom edge for the doors to seal against, with a silicon gasket. I used an oscillating saw to cut the bottom of the astragal so the astragal won’t hit the bump threshold. In my last house I had Anderson Architectural French doors. What I loved is that it was a single unit that included a gasketted seal on the bottom. Essentially a jam, just like on the top and sides. You could turn a hose on for an hour and you would not get a drop of water inside. They key is that the bottom has a jam too. So when I searched for a fix for my shitty-installed french doors on my new house, I wanted to reproduce this solid edge seal on the bottom. And after much searching I found the MD bump threshold. In addition I replaced the door shoes with M-D Building Products 43337 M-D... https://www.amazon.com/dp/B00PKSFEAI?ref=ppx_pop_mob_ap_share And I replaced the drip caps: M-D Building Products 68734 1-7/8-Inch Vinyl - 36-Inch DB037 Door Sweep with Drip Cap, Bronze https://www.amazon.com/dp/B001M58S8I/ref=cm_sw_r_cp_apip_pKixN4pHg3L89 I also recommend this adjustable stripe plate which helps make sure your door latch engages at the right place so you get that satisfying “thunk” when you close the door and feel it latch into place at exactly the right place for the door bottom to seal tightly against the bump seal. Defender Security U 9488... https://www.amazon.com/dp/B00D2K39BM?ref=ppx_pop_mob_ap_share Overall, fixing a shitty French door installation isn’t easy. But if you are weekend warrior, then installing a bump seal might be for you!

One of the things that gets me all twisted around in these types of choices is the historical context. The most appropriate choice from a decorative standpoint may not be the most appropriate choice from a historical standpoint. The most appropriate one may not be the one that looks better. But if you are changing it out of necessity, maybe letting the historical trump the decorative is kind of revisionist anyway because it's not really historical, it's a replacement. See how I can twist it around? But part of the issue is that in the US there is such little historical fabric. I was talking to a patient from England who said that the house she grew up in was 500 years old But as far as the interiors went, they did not necessarily pick a bathroom tile or fixture based on needing to look "appropriate" in a 500 year old house, because what IS such a thing? Here, we try to preserve each element because of its rarity, but when it comes to having to Replace, what then? Maybe if you are replacing it with something that was not there to begin with (I doubt there was a marble facing on the firebox on the second floor of a house like this) --maybe you can replace it with whatever you like. (?)

I’m not a pro so I am reluctant to advise on this, but here goes: Patching with drywall is probably the best choice. Drywall can be such a pain in the butt. So messy! I think that 1 inch gap may be too big for any type of paintable caulking, and the caulk would fall behind the wall, but others may be able to chime in on this. If you could find a piece of molding (small-thin) to add into that crack, with paintable caulk to make it blend in, it may work, but it not done “right” it could detract from the stone and look cheap. Also should paint it the same color and sheen as the walls to keep it from “popping”. If your stone sticks out some then you could get molding that is concaved (I don’t know what it’s called). This is all I can think of. I hope you are able to find a solution that doesn’t detract from your beautiful stone!

DON'T DO IT! I grew up in a house for the first nearly 20 years of my life that had a see-through fireplace with glass only on one side and a chain screen on the other. The reason they don't build these is because they cannot draw properly, at least based on what I understand. Your house will be filled with smoke if you ever want to actually use the fireplace. We had to use our fireplace for school art project displays because otherwise we never could use it for anything but display. A professional fireplace consultant that my parents hired came out to see if anything could be done, and it really couldn't. They're just not great ideas unless maybe you put gas logs, but I'd be concerned about proper drafting even with that.