Marine Le Pen exults after being reelected leader of France's National Front party in November. (Robert Pratta/Reuters)

In the aftermath of an attack on the French satirical newspaper Charlie Hebdo and with reports that authorities are closing in on the suspects, France's most iconic far-right leader has called for a referendum on reinstating the death penalty.

"I want to offer the French a referendum on the death penalty," Marine Le Pen, leader of the National Front party, told France 2. "Personally, I think that possibility should exist."

Execution was long a part of the French legal system: The infamous guillotine was used right up until 1977, when the last execution occurred. However, the death penalty was abolished in 1981; the change was enshrined in the constitution in 2007. France also leads the international campaign to end the death penalty, arguing against the practice at the United Nations and on other international forums. "The death penalty is not justice, it is a failure of justice" is how the French permanent mission to the United Nations puts it.

Le Pen has called for a return to the death penalty before, but in the nationwide shock after the Charlie Hebdo attack, she may well have more momentum. Under her leadership, the National Front has moved away from its more traditional far-right roots to become a populist right-wing party with a particular focus on law and order and immigration, and has gained mainstream support.

In particular, the party has taken aim at France's large Muslim minority. After the Charlie Hebdo attack, Le Pen renewed criticism of political Islam. "It is the Islamists who have declared war on France," she said in the France 2 interview, adding that France needed "to take the measure of the threat, not minimize it, not be in denial or hypocrisy."

The National Front has made political gains after similar attacks. When Islamist terrorist Mohammed Merah killed seven people in Toulouse and Montauban, it boosted support for Le Pen, Jim Shields, head of French studies at Aston University, tells Bloomberg. And with the popularity of François Hollande's Socialist government hitting remarkable lows, the National Front may well make gains again. In September, Le Pen topped presidential polls for the first time ever (though she is still likely to lose in a hypothetical runoff election).

The French public has been split on capital punishment in recent years (one poll from 2013 found that 50 percent supported reinstating the death penalty). However, the reality of reinstating it might prove complicated. France is party to many agreements that do not allow capital punishment, including the European Convention on Human Rights.

Whatever political gains might be made by the National Front, they are unlikely to be in the spirit of Charlie Hebdo. Although the newspaper may be more famous for its cartoons insulting Islamist hard-liners, it also frequently took aim at what it saw as Islamophobia among the French right: The paper's latest cover satirized the author of a book who imagines a France under Islamist rule by 2022. The paper also often mocked Le Pen for her views on immigration: