Radouane Lakdim, a 25-year-old Moroccan-born French national, had been on a list of suspected extremists since 2014 and was being monitored, leading to criticism of the security services from some politicians over their failure to prevent the attack.
Lakdim killed four people and injured four others on Friday in three separate shootings in the towns of Carcassonne and nearby Trebes, where he took hostages at a supermarket before being shot by anti-terror police.
The police source, who spoke on condition of anonymity, said that Lakdim had been sent a letter in March asking him to arrange a face-to-face meeting with agents from France's domestic intelligence agency DGSI.
Since the violence, police have arrested Lakdim's 18-year-old girlfriend, a radicalised Muslim convert, as well as a 17-year-old friend.
French President Emmanuel Macron will lead a national commemoration on Wednesday for hero policeman Arnaud Beltrame, who agreed to swap himself for a hostage inside the supermarket but was then killed by Lakdim who slit his throat.
The fact that Lakdim was on France's terror watchlist has led to accusations from the right and far-right that Macron's government is too soft on Islamists, while far-right leader Marine Le Pen has called for the interior minister to resign.
Experts point out that France has around 20,000 people suspected of being Islamic extremists and security forces have been successful in thwarting a series of attacks in recent years thanks in part to tough new anti-terror laws.