Appointments to the federal courts (Federal Court of Appeal and Federal Court Trial Division
) that have jurisdiction for all of Canada are made by the Governor General on the advice of the government.
The answer is yes, if he is a Treaty 8 Indian, at least according to the Federal Court Trial Division
(you can well imagine that the case will go to the Federal Court of Appeal and then on to the Supreme Court of Canada no matter what the ruling).
For example, there is presently in the Federal Court Trial Division
in Alberta, a case where the Sampson Indian Band is suing the federal government for the failure to be a prudent trustee in the management of its oil and gas revenues.
Sakimay Indian Band Council (1999) was argued before the Federal Court Trial Division
earlier this year.