There is no "Firefox database" beyond the data that is saved in the Firefox Profile on the device - with bookmarks being in the '''places.sqlite''' file in the Profile folder. '''If''' you were connected to Sync before reinstalling your Operating System, Sync should be able to "sync" your data back to that PC. That said, it is imperative that you don't change your Sync / Firefox Account Password before your data is recovered from the Sync server. When the user requests a new Password for their Firefox Account, the data for that account is cleared from the Sync server; and there is no way to recover from that, as there are no backup points saved - there is one data set saved by Sync.