Is there a noun form of the word "archaic"? The closest word I can think of is "old-fashionedness" but it seems rather clumsy.
“New” is to “novelty” as “archaic” is to passé
passé dated; out of style; old-fashioned
There are two uses of the word novelty. One is for an intangible characteristic of something, and the other is for the thing itself. Your suggested answer of "old-fashiondness" suggests you're thinking of the first usage.
In that case, I'd suggest quaintness. From dictionary.com we have
quaint adjective, quaint·er, quaint·est.
- having an old-fashioned attractiveness or charm; oddly picturesque: a quaint old house.
with quaintness as a derived form.
However, I believe that UK and American usage of quaint may be different. I'm answering from an American perspective.