The small groups, Mouvement Quebec francais and Mouvement Montreal francais, intend to make themselves heard at a Jan. 7 game against the Tampa Bay Lightning.
They are upset at the Habs for hiring a coach who can't speak French, ex-NHL forward Randy Cunneyworth.
They will hand out small Quebec flags outside the Bell Centre and encourage fans to wave them throughout the game.
It has been decades since the Habs, traditionally celebrated as French Canada's team, have had a non French-speaker as coach.
Some of the team's most legendary Anglo coaches of the '60s and '70s, like Toe Blake and Scotty Bowman, could get by in French.
Nationalists are seizing on this latest move, arguing that it proves that Quebec is sliding backwards.
"We will give fans Quebec flags and, by waving them during the game, they can make their opinions felt," the groups said in a statement.