No one knows how Franklin died. However, the conditions of his death are a bit suspicious:

1. No grave was found. While wintering in Beechey Island they buried their dead, but no grave was to be found for Franklin. He was like Madonna in his day, I highly doubt they would toss his body over board.

2. He was known to wear his medals like Nelson. However, they were found on his cabin by the Inuit who looted his ship, if I remember correctly.

Answering your question, Franklin died along with a dozen or so of other people. A note was left on the cairn saying "All is well", some days later the note was changed saying that several people died along with JF. It doesn't say why, but its already the most deadly expedition to date.

Under these circumstances I would say a bear attack is most unlikely. It also worth of note that JF was fat, old and out of shape to lead an Arctic expedition. A heart attack would be more plausible than a furry animal.

An Inuit attack is certainly a possibility like many speculated at the time. However, Inuit at that area were pretty friendly and lacked numbers, which would almost in certainty dissuade hostilities.

Scurvy is unlikely. Generally, scurvy would kick in by the third year or so (when lime lost the antiscorbutic properties) and afflict mostly the seamen, not officers. The latter had preferences in caught game (fresh food) and exempt from physical exertions.

On the same note, Sir Parry had the idea to cultivate mustard on his cabin during Arctic expeditions, which reduced the scurvy cases to none. Since those two were friends and JF asked Parry advice before (his first land expedition), I'd assume he grew mustard as well.

In truth? The ship's logs were destroyed by the Inuit. We'll never know...