After losing their bid in March 2014 to have the law ruled unconstitutional, counsel for Imperial Tobacco, JTI-Macdonald and Rothmans Benson & Hedges told the Quebec Court of Appeal the legislation "handcuffs" them.
In 2009 the Quebec government passed a bill aimed at making it easier for the province to argue its case against tobacco companies.
The law states the government does not have to categorically prove a direct link for all patients between their illness and exposure to tobacco products.
Quebec sued the companies in 2012 for $60 billion to recoup the health-care costs of citizens it says are a result of smoking.
Lawyers for the three firms told the appeals court the law prevents them from having access to a fair trial.
"We're going to have a rigged trial," said Simon Potter, who represents Rothmans. "The dice are loaded."
The law eliminates the right of tobacco companies to a "full and equal, public and fair hearing by an independent and impartial tribunal," as guaranteed in Quebec's Charter of Human Rights and Freedoms, their lawyers said.
Benoit Belleau, a lawyer for the government, argued the 2009 law balances the scales between the province and the tobacco firms.
Moreover, the province still has to prove the cigarette companies are at fault, Belleau said.
The Quebec government claims the firms falsely advertised their products by omitting to mention the dangers of tobacco and acted deliberately to mislead smokers.
The appeals court will rule at a later date.
Thursday's hearing came a few weeks after Big Tobacco was ordered to pay $15 billion to smokers in Quebec in what is believed to be the biggest class-action lawsuit ever seen in Canada.Suggest a correction