Nevertheless, it may well be possible that this library could, at least to some extent, be reconstructed. Copies of the official narratives of previous polar expeditions would certainly have been included; a standard nautical ephemeris and other reference works surely have been provided. Evidence may be lurking in all kinds of places, and Google Books and WorldCat could help us track down specific editions.
And now there is a perfect venue for such a collective undertaking: the LibraryThing Legacy Libraries project. They already have a catalog of the books aboard HMS Beagle, as well as several other vessels, and I've now created a catalog page for the lost library of Franklin's ships. It's fairly easy to add books -- the system will even look them up in the British Library or other catalogs and automatically fetch details. The criteria for inclusion should be (1) Books mentioned as being aboard by crewmembers or visitors to the ships at any time from their outfitting to the point at which the last letters were sent home from Greenland; (2) Books actually recovered by McClintock and other Franklin searchers; and lastly (3) Books which it can be reasonably inferred were aboard based on period evidence -- e.g. the statement that they had aboard all the previous printed narratives of British polar explorers. You can see that I've started to tag the books.
If anyone is interested in contributing, just drop me a note and I will send you the details so that you can log on, edit, add, and contribute.