"But they are not helping me", Carlos Osma, a 16-year-old from Sudan told the AFP news agency, before boarding a bus.
France and Britain are engaged in a diplomatic spat over who should take care of the young people relocated from the Jungle.
A first bus carrying 43 minors left the area around 8:30 am (0730 GMT) for the southwest, rapidly followed by a second one.
Junior Brexit minister David Jones told a parliamentary committee on Tuesday that Britain had given shelter to more than 300 children since October 10, but said there had been a pause in the process of admitting children while the camp was closed.
"The challenge now is to implement the terms of the agreement we concluded with the British", Cazeneuve said.
Dozens of British Home Office officials, including Border Force staff, were in Calais on Wednesday and will visit the 60 temporary housing centers dedicated to unaccompanied children to assess their asylum requests.
Around 200 migrant children were brought to Britain this month to be reunited with their families already over here. We will need assistance with travel documents out of France.
He said: "The situation for the children in France is chaotic, violent and unsafe".
"There are people out there who are willing to open up their homes to child refugees and we frequently receive emails and calls from members of the public including individuals, couples and families, expressing their will to actively respond to this crisis", he said.
Michel Aoun: Political survivor finally returns to power
He also thanked Prime Minister Tamam Salam for his leadership during the challenging period in the country. Lebanon has been without a president since May 2014 when former president Michel Suleiman left office.
After initially dragging its heels on the issue, Britain in mid-October speeded up the transfer of child refugees.
The United Nations' Committee on the Rights of the Child slammed both governments for disregarding the child migrants' best interests.
It said neither government could claim it was caught off guard by the situation, adding: "The failures regarding the situation of children in Calais are not isolated events but highlight the shortcomings of a migration system built on policies that are neither developed nor implemented with child rights in mind".
After the closure of the Calais camp, Hollande last week vowed to tear down any improvised migrant camps, saying France "will not tolerate" the sites any longer.
Migrants from the Mideast and Africa converged on the jungle camp in hopes of crossing the English Channel to Britain.
"Then there will be no one at the end of the day", said Steve Barbet, spokesman for the Pas-de-Calais region.
Charity workers criticised the plans to remove the shipping container site.
Kilpin was in the Calais Jungle last week and witnessed the demolition of the camp. How will the state look after them?