Layers of dirt on beautiful buildings? They're several hundred years old.
Felt quite unsafe even in good neighborhoods? I spent all last week there, on foot, at all hours alone and never once felt unsafe. It occurs to me now that maybe that's my male privilege so apologies if that's not the case for you but Paris is the greatest city in the world as far as I'm concerned.
As a Parisian, I can sadly attest that the city is currently disgustingly dirty, that it has been getting worse and worse in the five years since I moved there and that London is indeed a lot cleaner.
Paris suffers from a lot of incivilities, very lax policing, the current mayor puting cleanliness as a non priority and extremely poor supervision of the existing cleaning crews.
It has become such a pain point for Parisian that cleanliness is likely to be the main issue of next year electoral campaign.
May be the non-touristy areas are also considered dirty by you, but I'm an American, where we treat public places like shit but make sure interiors and the entrances near parking is pretty and the rest of the fucking street is trash since no one other than me apparently walk it. To me, the "grime" I see seems normal if not a little nicer than any city in Ohio.
I have to admit that when I went back to Paris 2015, the one thing that struck me was the dirt on the buildings like "le Louvres"'s musueum façade on the Rivoli street. It looked almost black. I actually did not really notice when I lived there, maybe it worsen.
Also I agree with you that Paris is a dirty city and London (at least the tourist areas) is much cleaner. There are a lot of incivilities in France and cleaning services are not known for their efficency.
As for safety, I also agree even if I have read that there has been many knife or moped attacks in London recently.
The stones being dirty is another issue. A lot of white stone will get darken by car pollution really quickly and cleaning those is a never ending process until fossil fuel is completely banned. The speed at which the the stone will get dirty as the the price of cleaning it wihtout damaging it differs a lot depending on the type of stone. I know that around the Loire valley, cleaning tuffeau is a huge pain.
Talking about the Loire valley, I lived in Tours also and It's true that this is very difficult to clean, if I'm correct the best technique is to use a laser but it's slow and expensive.
[1] https://www.theguardian.com/cities/2017/jul/24/revealed-pseu...