So I have good news and bad news.
Recognizing it as a historical landmark would, essentially, take too long, and it's due to close before that paperwork could be processed.
The good news is, there are actually two older bookstores still in operation (my original source was mistaken).
Livraria Bertrand can be found in Lisbon, Portugal, and was founded in 1773, and Galignani is in Paris, France and opened in 1856.
So if you're like me and you thrive in ancient bookstores, there's still hope.