About 200 riot police surrounded the camps housing migrants from Africa, the Middle East and Asia after a deadline to leave expired.
The Governor of the Pas-de-Calais region, Denis Robin, cited insanitary conditions in the camps and a scabies outbreak that he said was beginning to spread into the town of Calais.
Migrants' representatives were said to be in talks about whether they would accept an offer from the authorities of being rehoused elsewhere in exchange for a promise they would not be arrested.
Only one migrant so far has reportedly accepted this offer. They are thought to be reluctant to take alternative accommodation outside Calais as they hope to get into Britain.
The French government closed the Sangatte Red Cross centre, near Calais, in 2002 after repeated lobbying by the then home secretary David Blunkett. The camp was said to have been a staging post for thousands of migrants entering the UK illegally.
"This is sad, and it changes nothing," said Jalal, an Iraqi in his 20s who watched as police moved in.
"I'll move my tent somewhere else ... but I am staying put [in Calais].
"What else can I do? I will try again to make the crossing. I did not come here just to give up now."