It isseems likely lead poisoning was a factor (if not the definitive factor) in why Franklin's men did not approach the Inuit.
Over the course of months, Franklin and his men were poisoned either by the lead solder leaching into their canned food or the solder from their water-boiler. Chronic lead poisoning causes brain damage, which results in disordered thinking, stupor, and impairments in memory and concentration. We see evidence of this in the items recovered from the "boat place", which is where some of the survivors died trying to walk to the nearest Hudson Bay outpost. The lifeboat the men were dragging was loaded with things like soap, combs, books, and slippers. No rational man would try to drag a lifeboat weighted down with such things across a thousand kilometers of tundra.
Simply put, by the time Franklin's men realized they needed help (when their food ran low), they were too demented seek it.