Original reference (1846):

Sometimes I shouldered my gun and ranged about the forest in search of game, and occasionally took a swim in the sea. I was ignorant at the time, however, that there were sharks in the Gulf of St. Lawrence, else I should have been more cautious. The Indians afterwards told me that they were often seen, and several gentlemen who had lived long on the coast corroborated their testimony. Several times Indians have left the shores of the gulf in their canoes, to go hunting, and have never been heard of again, although the weather at the time was calm; so that it was generally believed that shark [sic] had upset the canoes and devoured the men. An occurrence that afterwards happened to an Indian renders this supposition highly probable. This man had been travelling along the shores of the gulf with his family—a wife and several children—in a small canoe. Towards evening, as he was crossing a large bay, a shark rose near his canoe, and, after reconnoitring a short time, swam towards it, and endeavoured to upset it. The size of the canoe, however, rendered this impossible; so the ferocious monster actually began to break it to pieces, by rushing forcibly against it. The Indian fired at the shark when he first saw it, but without effect; and, not having time to reload, he seized his paddle and made for the shore. The canoe, however, from the repeated attacks of the fish, soon became leaky, and it was evident that in a few minutes more the whole party would be at the mercy of the infuriated monster. In this extremity the Indian took up his youngest child, an infant of a few months old, and dropped it overboard; and while the shark was devouring it, the rest of the party gained the shore.

Assessment: This story rings false for at least three reasons. (1) First and foremost, the same account² is also told of an Inuit family in the Arctic. The sole differences are that the victims were traveling aboard a kayak (instead of a canoe), and the assailant is a Greenland shark. In both cases, the father sacrifices his youngest child without any apparent hesitation, which may be a reflection of a prejudiced and fictitious view of the indigenous peoples of Canada that is characteristic of the writings of many European explorers of the time. (2) The only shark likely to attack a boat in the fashion described by Ballantyne, and which is known to frequent the area, is the white shark. A birchbark canoe would offer little protection against a determined attack by a sizeable white shark and would quickly sink if significantly perforated. (3) The story is inconsistent. In one sentence, Ballantyne describes the canoe as small—although carrying two adults and several children—but then claims it was too big for the shark to capsize. The Nunavut story is of the same nature. (1) A sealskin kayak is an even more fragile watercraft. (2) A Greenland shark would be physically impeded from attacking a shallow draft kayak unless it were swimming upside down and biting from underneath. It is thus our determination that both reported incidents (Moisie and Nunavut) are almost certainly fabricated folk tales or distorted versions of other stories.

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References:
¹ Ballantyne, R. M. (1848). Hudson’s Bay, or Every-Day Life in the Wilds of North America. William Blackwood and Sons, Edinburgh and London. 353 p.
² Van Grevelynghe G., Diringer A. et Séret B. (1999). Tous les requins du monde. Collection Les encyclopédies du naturaliste, Delachaux et Niestlé, Lausanne (Suisse). 336 p.