The beef stems from a brouhaha involving one of his judges over a ruling written in English in a case where the evidence was heard in French and the accused was a unilingual francophone.
Superior Court Justice Karen Kear-Jodoin wrote her decision in English this year after both parties agreed in April 2014 they had no issue with it.
Defence attorney Frederic Allali later wrote a letter to Kear-Jodoin and copied Chief Justice Francois Rolland, complaining about the English-only judgment for his French-speaking client.
Rolland wasn't happy with the content and tone of Allali's letter and filed a complaint with the Quebec Bar.
The story spilled into the media and Rolland subsequently wrote a letter to the editor of a newspaper replying to a column by former Bloc Quebecois Gilles Duceppe on the matter.
Imperatif francais and Societe Saint-Jean-Baptiste said in their complaint that Rolland should not have publicly commented on a matter that was the subject of litigation.
The groups say they aren't happy with the English-only judgment.
"Imagine if, in English Canada, a judge dealing with two English parties rendered a judgment exclusively in French," Societe president Maxime Laporte told a news conference Friday. "Just imagine the outcry that would be created by such a situation."
Laporte concedes the parties initially agreed to Kear-Jodoin's request to write her judgment in English, but argues they did so because they didn't want to offend the judge.
The groups are also asking Culture Minister Helene David, who is responsible for the French Language Charter, whether she finds the situation "normal."
Allali says he's happy with the support but will leave it up to the Quebec judicial council to rule in the case.