Fossil's "file format" is not intimately tied to SQLite: https://fossil-scm.org/home/doc/trunk/www/fileformat.wiki
That being said, it's the only existent implementation and none other are planned. If you'd like to port it to PostgreSQL, go for it, but it probably would lose a lot of the appeal of being a distributed version control system.
I thought that Fossil did or at least aimed to support different SQL RDBMSes. Did that go away at some point?