The van crashed into one of three lorries that had been stopped by the improvised barrier at 3.45am, bursting into flames, police said.
The accident took place on the A16 motorway about 15km from Calais.
Nine Eritrean migrants found in one of the lorries were detained and are expected to be charged with involuntary homicide, disrupting traffic and endangering people's lives.
Migrants return to Calais
Migrants place barriers made up of tree trunks and other large objects on roads to slow down lorries headed for the UK and try to hide in them.
The practice was common, especially on the Calais ringroad, before the clearing of the Jungle camp in October 2016.
It has reappeared since the end of May as migrants return to the area.
Between 400 adn 600 migrants are now living in and around Calais, hoping to sneak into Britan.
Interior Minister Gérard Collomb announced at the beginning of the month that an extra 150 police and gendarmes would be sent to the area.