Not a file sharing, but distributed DHT-like database HASH=BLOCK
What you're looking for is
Freenet. Aside from the anonymity (which is neither needed or maybe even desired for blockchain storage) Freenet is a large operating content-addressed, redundant distributed filesystem with some unique properties such as good resistance to data loss even under the condition of nodes coming and going randomly, with no explicit coordination or configuration. The Freenet developers are aware of Bitcoin and are aware of how Freenet and the potential synergy between the two projects, and I think they only thing that's missing is interest for some type of collaboration to happen is some programmers on the Bitcoin side to take an interest in them.