You could see the Crillon is still being renovated. That twin structure you got on your last picture is called hôtel de la Marine.
It's been a little while since the last time I crossed the square. I'd like to have scaffoldings and workers to the Crillon visible to everyone, so we all could see their work, but for some silly reason they hide it all behind some fence showing a picture to scale of the façade.
Hiding the work is dumb.
I find these 2 twin buildings from the 18th century are the most responsible for the monumental aspect of the Concorde square with the Neoclassical Madeleine church (that's slightly more recent, from the early 19th century) in the background, as seen from the square on your 1st picture of the previous post. Good quality pictures BTW.
Too bad cars still occupy most of the public space right there, isn't it? It could easily be something lovely to pedestrians and bikers. Either locals or tourists would enjoy it.
I forget who purchased and is renovating the Crillon hotel. An investment fund from the Middle East, I believe... Yes, it's now owned by the crown of Saudi Arabia. I think it's been some of their strategy lately. They've been purchasing some historic properties like this over here, foreseeing a potential decline of the oil industry and converting a bit of their assets to solid estate like this.