Scuffles broke out in the Jungle camp in Calais less than an hour after French authorities began a fresh round of processing refugees and migrants to be driven away.
Some 1,918 residents packed their bags and were taken by bus to 80 accommodation centres on the first day of the mass exodus, the French Interior Ministry said.
Another 400 unaccompanied minors had registered and were being housed in heated shelters at the camp.
The small spat is thought to have started as unaccompanied minors were being separated from the main queue and taken to the front.
Someone shouted into a loudspeaker: “Sit down, the door is closed. Stop pushing”, while cries of “Help, please help” were heard as people started to panic.
Migrants and refugees believed to be minors could be seen crouching down by metal barriers while police formed a protective circle around them.
The gate to the processing centre was temporarily closed while the chaos continued.
Numbers were fewer than on Monday, when hundreds of camp residents with holdalls, rucksacks and wheeled bags queued up in the dark more than an hour before the registration centre opened.
Speaking on Monday evening, French Interior Minister Bernard Cazeneuve said: “This is an operation we want to be peaceful and under control. So far it is.”
On Tuesday, many were studying sheets of paper given to them by aid workers which included information in Arabic and English and a map of France.
A further 85 buses are expected to arrive on Tuesday and Wednesday, with officials saying the entire operation will last at least a week.
A demolition team is due to begin dismantling the squalid settlement on Tuesday but bulldozers are not expected to be brought in.
Meanwhile, France’s ambassador to the UK has insisted her country will not tolerate another Jungle camp springing up in Calais.
Sylvie Bermann said the French government wants to show migrants that the port city is a “blind alley” which will not gain them access to Britain.
She told the BBC Radio 4 Today programme: “The government is determined to stop people coming back to Calais. We won’t let them come. It has to be clear that Calais is a blind alley, and you can’t come to this country. If they are refugees they will go to other centers.
“We will leave policemen there for the time being. There are more than 2,000 policemen there.”
As French authorities continued to dismantle and empty the squalid camp, the ambassador insisted that Britain had been asked to take all the unaccompanied children from the Jungle settlement.
Ms Bermann said 600 children are now in special centres in Calais waiting to be processed.
“What we asked the British Government is to take all unaccompanied children, and they said they want to process the cases and check if they have families here. It’s impossible for the French to know if they really have families in the UK. So we gave the list to the UK Government and now they will have to process,” she said.