Almost 2,000 migrants have been bussed away from the "Jungle" in Calais as French authorities clear the camp.
At least 7,000 people have been living there in squalid conditions.
Migrants queued peacefully to be processed, but there are concerns some will refuse to go because they still want to get to the UK.
Almost 200 children from the camp have been brought to the UK, some of them under the "Dubs" arrangement, according to UK Home Secretary Amber Rudd.
The number includes 60 girls who were at high risk of sexual exploitation, she said.
But the process of transferring some of the estimated 1,300 unaccompanied children from the camp was halted on Monday at the request of the French.
The dismantling of the camp is expected to start on Tuesday.
Read more on this story:
Long queues formed earlier outside reception centres in the camp as the French authorities worked to determine whether individual migrants were with family members or travelling alone, and whether they were deemed to be vulnerable.
After processing, they boarded buses to different parts of France where they will be given the opportunity to claim asylum, or face deportation.
Britain still within reach: By Clea Caulcutt, BBC News, Saint Germain-sur-Ay
Forty-five migrants, all young men from Afghanistan, are settling into the Miramar hotel, an empty holiday centre that looks out to sea.
At the local pizzeria, residents have gathered to vent their discontent. They complain that the migrants will disturb the tranquillity of the resort. They are also worried that the young men will be unsupervised and break into homes that have been closed up for the winter.
Less vocal are those who don't mind the arrival of the Afghan migrants, those who think it's only human to welcome those who have spent so many months in the squalor of Calais.
For the migrants, it should be a short stay. They will be encouraged to claim asylum in France and then maybe move onto more permanent housing. But even here, several hundred kilometres from Calais, the allure of the UK is still strong.
From the hotel you can clearly see the island of Jersey - British shores are still without reach.
At least 40 of the 60 coaches planned to transport them have now left, according to BBC correspondents at the scene.
In a statement (in French), French Interior Minister Bernard Cazeneuve said 2,318 migrants had been "given shelter" on Monday.
He said 1,918 adults had been taken away on 45 buses to 80 reception centres.
Four hundred minors were transferred to "provisional reception centres" within the camp, he added.
The first step of the clearance had taken place in a "calm and controlled manner", he said.
Some volunteers complained earlier that the migrants had not been given enough information about the plans and warned of a sense of confusion and chaos.
About 7,500 beds are being made available in 450 centres across France. So far migrants have been taken to the regions of:
- Pays de la Loire
- Grand Est
- Nouvelle Aquitaine
'My dream is dead' - at the Jungle with the BBC's Gavin Lee
Rue des Garennes links the Jungle camp to the new migrant processing centre, and is a street of suitcases and resignation.
At 05:00, three hours before the clearance operation was due to start, groups of refugees and migrants began to form a queue. Since then, a mass exodus from the camp, and hundreds are now lining the road waiting for a coach to take them away.
Towards the back of the queue is Adil from Sudan, carrying two bags, a football and a guitar. "My dream is dead, the people you see here, they are broken. We can't believe it's over."
Inside the camp, aid workers from Care for Calais are moving tent to tent, warning migrants that if they do not leave, they will be arrested. The police presence is large, with many huddled in riot vans, keeping out of the cold, and making the most of the calm.
Children will be housed in the camp's converted shipping containers while the rest of the Jungle is dismantled.
The "Dubs amendment" rules allow particularly vulnerable children - such as girls and those under 13 - refuge in the UK, even if they do not have family already in the country.
The operation to clear the tents and shelters is expected to take three days.
The French interior ministry said "police might be forced to intervene" if there was unrest during the demolition.
There are reports that British activists from the No Borders group have travelled to the Jungle to try to disrupt the process.
Violence has frequently broken out as migrants, mainly from Africa and the Middle East, attempt to board lorries bound for the UK and clash with drivers and police.
Why do migrants want to come to the UK?
Most believe there is a better prospect of finding work. Many want to claim asylum, although others want to enter incognito and remain as illegal workers.
The language issue is also important - many speak English but do not have a European language. Some also have relatives in the UK and that is a big draw.
Some are attracted by a belief that there is better housing and education available.
Some commentators believe illegal migrants also perceive Britain as a "soft touch" for benefits and a better place to find "black economy" jobs, although studies do not necessarily back up this view.
A UK-funded wall 1km (0.6 miles) long is being built along the main road to the port in an attempt to deter would-be stowaways. The UK government is reported to have contributed about £1.9m (€2.2m) to the cost of the wall, which is due to be finished by the end of the year.
Speaking to the BBC, the head of the organisation that runs the port of Calais, Jean-Marc Puissensseau, said business had declined due to attempts by migrants to board trucks.
"The port has been really suffering [for] more than one year, because each night there were some attacks, or [migrants] were throwing branches, trees, everything to try to slow down the traffic and then to get into the trucks," he said.
What is the Jungle?
- The Jungle camp is near the port of Calais and close to the 31-mile Channel Tunnel
- Officially about 7,000 migrants live in the camp. The Help Refugees agency said the final population ahead of its demolition was 8,143
- The camp was halved in area earlier this year but the population continued to rise, and reports of violence have increased
- Many migrants attempt to hide themselves in cargo vehicles entering the Channel Tunnel
- The area has been hit by protests from both locals and truck operators
Last year more than one million migrants - many fleeing the civil war in Syria - arrived in Europe. Countries struggled to cope and division arose in the EU over how best to deal with resettling people.
An EU-Turkey pact to try to stop migrants crossing to Greece and moves by Balkan nations to close their borders have driven down the number of people using the so-called eastern Mediterranean route.
However, migrants from African countries such as Eritrea and Somalia as well as West African nations such as Nigeria and the Gambia are continuing to attempt the crossing from Libya to Italy.
Read more on Europe's migrant crisis:
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.