Two bulldozers and around 20 workers began destroying makeshift shacks, with 30 police cars and two anti-riot vans stationed nearby.
The situation was mostly calm, although one member of the British "No Borders" activist group was arrested.
"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, AFP reported.
She accused No Borders activists of threatening workers Friday, a day after a French court had given the green light to clear the southern half of the camp.
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.
Activists had appealed to the court to stop the evacuation of the Jungle, a grim shantytown on the outskirts of Calais where thousands of migrants and refugees have gathered in the hope of sneaking aboard lorries and ferries to Britain.
Local authorities, who have promised that no one will be evacuated by force, say 3,700 people live in the camp, and that between 800 and 1,000 will be affected by the eviction.
But charities say a recent census they conducted counted at least 3,450 people in the southern part alone, including 300 unaccompanied children.
The evicted migrants have been offered heated accommodation in refitted containers set up next door to the camp, but many are reluctant to move there because they lack communal spaces and movement is restricted.
They have also been offered places in some 100 reception centers dotted around France.
The migrants in Calais make up a tiny fraction of those fleeing war and poverty in the Middle East and Africa.
They try to climb on to lorries boarding ferries for Britain, which they are drawn to by family or community ties, because of a shared language, or because they think they have a greater chance of finding work there.