French police arrived in force to monitor the partial demolition of the Calais refugee camp on Tuesday - the date French authorities had hoped to finish clearing the area.
A spokesman for the area said on Monday that French authorities expect to finish clearing half of the camp nicknamed "Jungle" within days.
The demolition of the southern part of the camp began on February 29, when the French government won a legal battle against activists allowing it to dismantle part of the camp.
"Around 5.5 hectares out of the 7.5 that are to be dismantled are now cleared," the spokesman said.
Authorities offered the evicted refugees a place in heated tents in the northern section of the camp, or encouraged them to leave the area by bus for one of France's 102 reception facilities.
A shelter made of converted shipping containers - which opened earlier this year and is designed to hold about 1,500 people - is already full, the spokesman said.
Thousands of refugees have converged on Calais over the past year, hoping to find a way of getting across the Channel to Britain.
There are at least 3,450 refugees in the southern part of the camp, including 300 unaccompanied children, according to human rights groups. This is more than triple the official number of between 800 and 1,000.
The French police have used tear gas and beat refugees who did not comply with detention orders, according to Doctors without Borders (MSF).
Pierre, a nurse in the MSF clinic in the "Jungle," said that many people in the camp have suffered from breathing problems because of tear gas.