The man, identified by French police sources as 31-year-old Mohamed Lahouaiej Bouhlel, was not known by the Tunisian authorities to hold radical or Islamist views, the sources said.
Bouhlel was married with three children, they said. The sources did not say when he had last been resident in Tunisia.
Msaken is about 10 km (six miles) outside the coastal city of Sousse.
Tunisia's consul in Nice said one of the 84 victims of the attack had been identified as Tunisian national Bilal Labawi, and that officials were working to check for other Tunisian nationals among the casualties, state news agency TAP reported.
The Tunisian government issued a statement condemning the attack "in the strongest possible terms".
"Tunisia stands by France in its fight against terrorism and supports any measure taken by the French government to protect its territory and the security of its citizens and visitors," the statement said.
Like France, Tunisia has also suffered badly from militant Islamist attacks in recent years. On June 23, 2015, a gunman killed 38 people, mostly British holidaymakers, on a beach in Sousse, in an attack that dealt a heavy blow to its tourism industry, which accounts for eight percent of national output.
The ID card of Mohamed Lahouaiej Bouhlel recovered from the scene of attack
An attacker who drove a heavy truck into crowds in the French city of Nice killing at least 84 people came from the Tunisian town of Msaken which he last visited four years ago, Tunisian security sources said on Friday.
