In a letter dated yesterday, the signatories said they had "very serious worries concerning the security and well-being of unaccompanied minors and vulnerable adults".
Cazeneuve has pledged that all remaining migrants at the site, currently occupied by around 5,700 people according to official figures, would be given "dignified" shelter after the camp is cleared.
"We fear that the resources currently being deployed and the proposed responses are insufficient to ensure the effective protection of the most vulnerable, notably unaccompanied children," the letter said.
They said a poorly-organised clearance would put already fragile people into an even more precarious situation.
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The letter asked for all unaccompanied minors to be found shelter before the demolition begins, for a designated "safe zone" in the camp during the dismantlement and, that everyone eligible to join family in Britain be identified.
The signatories included 60 of the 650 MPs, including Liberal Democrat leader Tim Farron, Green Party co-leader Caroline Lucas, former deputy prime minister Nick Clegg and main opposition Labour finance spokesman John McDonnell.
It was also signed by two bishops and several members of parliament's upper House of Lords, including Paddy Ashdown, the former international high representative for Bosnia and Herzegovina.