Up to 2,000 migrants in the southern part for the sprawling site near the Calais Eurotunnel entrance have until 8pm local time (7pm GMT) today to leave their makeshift homes or face bulldozers being sent in.
A portion of them are set to be moved into heated shipping containers complete with beds which have been placed on the then vacant site, but there will not be space for everyone.
Charities have stepped in to demand the migrants are allowed to stay in their shanty town, using the plight of hundreds of unaccompanied children, mostly Afghan, to argue their case.
Refugee organisations are pinning their hopes on a court hearing due to take place in Lille this afternoon, just hours before the deadline.
A French judge is visiting the Jungle today to check out conditions for themselves before making a ruling on whether the eviction should go ahead.
Up to 1,000 people, many who have fled war, poverty and persecution, are said to be affected by the plans, but aid workers say the figure could be closer to 2,000.
The Help Refugees charity said it carried out its own analysis showing there were 3,455 people living in the affected part of the Jungle who face being “evicted from their homes in the midst of winter, without sufficient alternative accommodation on offer”.
A spokeswoman said: “Our concerns remain with welfare of the unaccompanied minors.
“We have had no assurances from the French authorities that they will conduct assessments to determine best interests of these children and ensure proper safeguarding is in place before removing them from the camp and the communities they know and trust.
“We urge them to delay the demolition of the southern section of the camp until these needs are met. Our concerns will be heard at the court in Lille.”
Over the weekend actor Jude Law, singer Tom Odell, actress Juliet Stevenson and comedian Khorsandi took to the stage at the Calais camp to fight for the refugees at a Leters Live event.
It came after 145 celebrities, including Idris Elba, Helena Bonham Carter and Benedict Cumberbatch wrote an open letter calling on Prime Minister David Cameron to help save children based there.
They want the Government to step in and allow unaccompanied children living in the camp to be reunited with their families, many of whom are already in the UK.
EuroTunnel has asked the British and French governments to reimburse it £22.6million for lost revenue during the cross-Channel migrant crisis.
The Channel Tunnel operator faced heavy disruption to its services last summer as migrants based at the Jungle Camp made repeated bids to reach Britain.