An operation involving elite police is continuing at the Super U shop, where others were wounded.
Reports say the gunman, who remains in the supermarket, pledged allegiance to the Islamic State group.
Earlier, a policeman was shot and wounded while jogging with colleagues in Carcassonne, a 15-minute drive away.
He was shot in the shoulder by the same suspect involved in the supermarket hostage-taking but is not critically injured, Yves Lefebvre, secretary-general of the SGP Police-FO union told the Associated Press.
Trèbes Mayor Eric Menassi told BFM TV that the gunman was now alone in the shop with one police officer, after other hostages were freed.
The suspect is said to be heavily armed and asking for the release of Salah Abdeslam, the most important surviving suspect in the 13 November 2015 Paris attacks, which killed 130 people.
Reports say the suspect is known to French intelligence services and that his mother is at the scene.
A security source told French news agency AFP that most employees and customers at the supermarket “managed to flee”.
Prime Minister Édouard Philippe said the situation was “serious” and that all signs pointed towards a “terrorist act”.
Hundreds of police officers have been deployed to the area, and the vicinity has been cordoned off.
Counter-terrorism prosecutors are leading the investigation but few details have been provided.
France has been hit with several deadly jihadist attacks since 2015 and has been on high alert since. A state of emergency put in place after the 2015 attacks in Paris was lifted in October.
In February, Salah Abdeslam went on trial in Belgium over a shootout in Brussels that led to his capture months after the Paris attacks. He is not expected to go on trial in France until 2020 at the earliest