Authorities have left just a few structures housing communal facilities such as mosques or canteens in the 7.5-hectare (18.5-acre) southern part of the camp.
Police had fired teargas to disperse protesters when the operation to raze the wooden and tarpaulin structures began on February 29th.
More than 1,000 people had lived in that part of "The Jungle" as they waited to try to scramble on to lorries waiting to board ferries or Channel Tunnel shuttle trains to Britain.
The migrants believe they have a better chance of finding work in Britain, and some have family ties there.
With thousands of migrants cleared from the southern part of the camp, there are fears that many have not taken up the advice of French authorities to either move to permanent accommodation in shipping containers or accept being moved to one of the welcome centres around the country.
While some of the migrants have moved into the shipping containers, others have headed for camps further along the coast. Hundreds also remain in the northern part of the Jungle.
Migrants' representatives warned the French government in a statement that it would be "unacceptable" to try to clear the northern sector as well.
The local authorities have stated several times that they want to limit the camp to 2,000 residents, but have stipulated that those who stay must move into the containers.
The camp made of containers can hold up 1,500 people and 400 places are also available to women and children in another centre nearby.
Hundreds of shopkeepers and restaurant owners from Calais held a protest in Paris on March 7th to complain that they have suffered heavy losses as a result of the presence of migrants in the port.
The Local France reported earlier this month how there was growing evidence the closure of part of the Jungle camp was pushing refugees and migrants to seek a path to the UK via ports in Normandy, including sleepy fishing villages.
There were fears that migrants would focus on getting across to the island of Jersey, just a 25 minute boat journey from Barneville-Carteret, a tiny port town on the picturesque Contention peninsula. (see map)