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"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.
"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."
The state wants to eventually reduce the population of the Jungle to 2,000 people.
Those being pushed out of the camp can go to one of around 100 accommodation centres elsewhere in France, or into refitted shipping containers set up nearby.
The containers have not proved popular with migrants, who say they lack communal spaces and restrict their movements, while local charities say they fail to meet international standards.
Conditions in other camps along the northern French coast are even more dire than those in the Jungle.
The French authorities have been gradually trying to shut down the Jungle, encouraging residents to head for proper centres elsewhere in France.
However, many of the residents have family or community ties to Britain and are reluctant to give up their dream of crossing the Channel.
A campaign spearheaded by celebrities such as actors Jude Law and Benedict Cumberbatch has called on the British government to let children from the camp be reunited with families in Britain and take responsibility for the "humanitarian crisis" in the Jungle.
Calais town hall has claimed the eviction is in response to "abuses" committed by migrants that had led to "an aggravated level of tension" in recent weeks.
It said camp residents were throwing stones and other projectiles at lorries and security forces on a daily basis, but also condemned members of far-right groups who loiter outside the Jungle to beat up migrants.
On Monday, six migrants were each given a month in prison for occupying a ferry in northern France in a protest calling for Britain to allow asylum seekers in.