No, “First Nations” does not refer to Inuit peoples, nor does it refer to the Metis. These three groups collectively make up what are called Aboriginal peoples in Canada by the constitution act of 1982. The other broad term you might use if you are not sure about, or are talking about several sub-categories or nations, is indigenous people(s). Or you know, just ask people how they want to be referred to.
"Indian" still has weight as a legal term in Canada because it is the word that was generally used in law prior to 1982.
In any case, the Inuit are fairly clearly not "first nations" because they are clearly not the first people to live where they live now; they displaced the Dorset peoples from most of Canada's arctic relatively recently when compared to the settlement of the Americas—recently enough for the Dorset to have had contact with viking traders, for instance. Inuit tradition calls the Dorset "Sivullirmiut" or "First Inhabitants".