The police operation comes two days before Besson is due to visit Calais for talks on the situation.
Besson said last month that trafficking networks are becoming increasingly sophisticated, and that more people had managed to cross the Channel over the past year or two.
France is struggling to control the tent city, which sprang up after a Red Cross shelter, the Sangatte refugee camp, was closed in 2002 following pressure from Britain.
London said the camp encouraged migrants to make the trip across the Channel and enter Britain illegally.
But migrants, including many from Iraq, Afghanistan and Eritrea, have continued to arrive in the region, with numbers building up in squatter camps in the woods around Calais.
Many of them speak English and believe it will be easier to find work in Britain.