More than 1,900 left the slum on Monday, ahead of work to tear down the makeshift shelters and eateries in the camp that has become a symbol of Europe's refugee crisis.
Some 400 youngsters are being provisionally housed in shipping containers in a part of the Jungle where families had been living, Interior Minister Bernard Cazeneuve said Monday.
An estimated 6,000-8,000 people, mainly Afghans, Sudanese and Eritreans, have been living in dire conditions in one of Europe's largest shantytowns in the hope of sneaking into Britain.
Early Tuesday, scores of minors awaited their turn to be interviewed by French and British officials.
Among them was Alaa, a 17-year-old from Iraq's second city Mosul, who said he fled his country with his 25-year-old brother when the Islamic State group launched its offensive into northern Iraq in 2014.
"We had no choice but to flee," he said. "If they want to kill you they kill you."
But life in the Jungle has been "really horrible," he said. "I had my phone stolen, I was beaten, I was threatened."
His brother managed to sneak into Britain and join an uncle there, but Alaa stayed back because "it was far too frightening and dangerous."
Cazeneuve said all unaccompanied minors "with proven family links in Great Britain" would eventually be transferred across the Channel.
'We're doing their work'
Britain has taken in nearly 200 teenagers over the past week, but the transfers were on hold Monday.
British interior minister Amber Rudd said London was contributing up to £36 million (40 million euros, $44 million) towards the operation to clear the camp.
The head of France's refugee agency, Pascal Brice, had harsh words for Britain's role on Tuesday.
"We're doing their work for them," he said on French radio, reiterating calls for Britain to take in the Jungle's minors.
Britain and France signed the so-called Le Touquet accord, which effectively moved Britain's border with France to the French side of the Channel, in 2003.
Christian Salome, head of the Auberge des Migrants (Migrants' Hostel) charity, said the transfer process was "working well" but he feared around 2,000 people "still want to reach England." The French interior ministry dismissed that figure as exaggerated.
Located on wasteland next to the port of Calais, the four-square-kilometre (1.5-square-mile) Jungle has become a symbol of Europe's failure to resolve its worst migration crisis since World War II.
More than one million people fleeing war and poverty in the Middle East, Asia and Africa poured into Europe last year, sowing divisions across the 28-nation bloc and fuelling the rise of far-right parties.
Brice said Tuesday that some 100,000 people will have sought asylum in France this year compared with 80,000 in 2015.
Those seeking to smuggle themselves into Britain, believing it offers better chances of work and integration than France, have been converging on Calais for well over a decade.
Over the past year, police have battled near-nightly attempts by migrants to climb onto trucks heading across the Channel.
The redistribution of the migrants is a risky enterprise for Socialist President Francois Hollande, six months before elections in which migration will loom large.
Some have opposed plans to resettle asylum-seekers in their communities.
In the eastern village of Chardonnay two dozen young Sudanese asylum seekers received a chilly reception on Monday.
Migrants wait to access the process centre during the evacuation of the makeshift camp 'the Jungle' in Calais, France, 25 October 2016. Source: AAP
Locals watched from a distance as the men got off the bus in the village, which will eventually host 50 asylum seekers among a population of just 200 villagers.
"This massive arrival of migrants, it's inappropriate," fumed resident Joelle Chevaux, out walking her dog.
'To start a new life'
But elsewhere people turned out in solidarity for the migrants, with rallies attracting some 200 people in Paris and 250 in the western city of Nantes, according to police.
Jean-Marc Puissesseau, chief executive of Calais port, told Britain's BBC radio he was "a very, very happy man" and hailed an end to the "constant stress" of drivers fearful of being ambushed by migrants.
Dozens of people have been killed on the road or while trying to jump onto passing trains.
Puissesseau warned that new camps would sprout up around Calais unless police remained vigilant.
"All I want is to go back to school, to start a new life," said Alaa, the 17-year-old Iraqi.
