1. Search for Franklin - Neatby, L.H. : A lucid and readable introduction to the subject for the "newbie" just starting out that is good for context. If you are already familiar with the subject to the extent that you know who Fitzjames is you may safely skip this and go to:
2. Sir John Franklin's Last Arctic Expedition - Cyriax, R.J. : A timeless classic, a little dated and conventional as Cyriax hated speculation. Published in 1939 so doesn't have the most recent findings, but still excellent.
3 . Barrow's Boys - Fergus Fleming : A great book to put the whole Victorian craze with exploration, and the Franklin Expedition, in a wider perspective. Fleming also brings the whole arctic enterprise alive with colourful descriptions of the actors. An easy read full of gems - after reading this you will have a deeper understanding of the men whose exploits are often recorded so matter-of-factly - you will never think of Lyon again without thinking of his tattoos!
4. The Voyage of the "Fox" in the Arctic Seas - McClintock, Francis Leopold : Can't beat the original search documents, reads a little slowly in spots until the relics are found but an essential source.
5. Schwatka's Search: Sledging in the Arctic in Quest of Franklin Records - Gilder, William H. : As valuable as McClintock, you can't really understand the evidence without reading it. A little flowery in tone (written by a journalist vs a Naval Officer), best read in this order for chronological reasons.
6. Deadly Winter: the life of Sir John Franklin - Martyn Beardsley : A very good biography of Sir John that sees him as a full person rather than a caricature. I tend to agree with Beardsley's conclusion but he is very fair in giving space to the alternative readings of Sir John's career and life.
7. North With Franklin: The Lost Journals of James Fitzjames - John Wilson : It is of course best to read Fitzjames' Journal in the original, but as that is difficult Wilson's fictional treatment is a good alternative and nice way to try to get the "feel" of what transpired.