parterre and port cochere?

Well par terre (two words not one) is a patterned dicvision of garden beds.
Port cochere I believe is a porch.

Neither of which I see on my pomme de terre iphone in the photos

A parterre is a formal garden constructed on a level surface, consisting of planting beds arranged to form a pleasing, usually symmetrical pattern, with gravel paths laid between.
(See building pics for large lawn separated by walkways)

A porte-cochère (/ˌpɔərt koʊˈʃɛər/; French: [pɔʁt kɔʃɛʁ] "coach gate"; also called a "carriage porch") is the architectural term for a porch- or portico-like structure at a main or secondary entrance to a building through which a horse and carriage (or motor vehicle) can pass in order for the occupants to alight under cover, protected from the weather.
(See building pics - cars can drive up to door under a covered entry)

Yes, now does all the french make you forget it's an average, cookie cutter, post war, brick co-op?

I'd stick to focusing on le parc central.

Maybe call the building, Oo.. Lala... Le Parc.

They don't use these fancy French terms up in C0lumbia C0unty.