"The date and circumstances of his death aren't yet known, but it appears he died in the summer of 2017," sources close to the inquiry told the AFP news agency on Thursday.
Hauchard, who grew up in a village in Normandy before converting from Catholicism to Islam, was just 22 when he was holding a knife to the neck of US aid worker Peter Kassig in a gruesome video from November 2014.
The video also showed the execution of 18 Syrians identified as military personnel.
France soon issued an international arrest warrant, and the US State Department added Hauchard to its black list of "specially designated global terrorists".
Investigators later found that Hauchard became radicalised online, joining jihadist forums under the moniker Abu Abdallah al Faransi ("the Frenchman").
He twice travelled to Mauritania between October 2012 and May 2013 for studies in Salafism, the highly conservative branch of Islam.
In August 2013 he left for Syria via Turkey, telling his family he wanted to "help the wounded" in the country's civil war, but in fact he was taken under the wing of IS recruiters.
"To show allegiance, you must first go to a training camp. The first stage lasts around a month. We do some training, we go on operations and after that we return to training. It's not just theory," he told a French TV station in July 2014.
A few months later IS released the video showing the execution of Kassig and the Syrian soldiers, in which Hauchard was shown with his face uncovered.
He emerged again in November 2015, a few days after the Paris terror attacks that killed 130 people, warning on Twitter: "Brazil, you're our next target," a reference to the 2016 Summer Olympics in Rio de Janeiro.
The French government says about 1,700 French nationals have left to fight alongside IS in Iraq and Syria since 2014.
More than 300 French jihadists, including 12 women, have been killed during the fight against IS in Iraq and Syria since then, while about 730 adults and 500 children are still there.
The interior ministry says 256 French jihadists have returned to France, along with 78 minors.
- with AFP