Images (below) from the camp showed workers pulling down the makeshift huts under the close watch of police.
"We are carrying out our orders so that the migrants leave the camp and we will continue this work this morning... so that the destruction work can continue calmly and that the migrants are not under pressure from the No Borders activists," said local authority head Fabienne Buccio.
Buccio said three-quarters of the shacks in the southern half of the camp were now empty after migrants were encouraged to leave in recent days.
Those organizations claim that French authorities have vastly underestimated the numbers of refugees and migrants living in the southern part of the camp and the alternative options lined up for those evicted are insufficient.
While local government chiefs say around 1,000 migrants will be affected by the clearing of part of the camp, groups like Medecins sans Frontieres have told The Local the figure is closer to 3,000.
The migrants and refugees have been given two official options by authorities - either move to an authorized part of the camp where places are still available or be moved to one of the 102 "welcome centres" around France.
However aid groups believe migrants, who are determined to reach the UK, are more likely to opt for a third option which will be to simply set up camp elsewhere in the northern port town.
"Around 500 to 1,000 migrants will just disappear because there is nowhere for them to go," Michel Janssens from the charity Medecins sans Frontieres told The Local last week.
"It's not human to do that. We are not fighting for them to keep the camp but for the occupants to be given adequate and humane lodging," Janssens added.
"All this will do is see hundreds end up living in clandestine camps."