At least six people died and more than 50 were rescued after a migrant boat trying to cross the Channel from France capsized early on Saturday, local authorities said.

Local mayor Franck Dhersin said a vast rescue operation was launched around 6am local time as dozens of migrant boats tried to make the crossing at the same time.

"Several of the boats were facing serious difficulties," he said. "Near (the coastal town of) Sangatte they unfortunately found dead bodies."

The maritime prefecture confirmed that there had been at least six deaths and said search and rescue operations were ongoing.

The Channel between France and Britain is one of the world's busiest shipping lanes and currents are strong, making the crossing on small boats dangerous.

Human traffickers typically overload rickety dinghies, leaving them barely afloat and at risk of being lashed by the waves as they try to reach British shores.

"We saved 54 people, including one woman," said Anne Thorel, a volunteer who was on one of the rescue boats, describing the migrants' frantic efforts to bail water out of their sinking vessel using their shoes.

"There were too many of them on the (migrant) boat," she said by phone as she returned to the shore.

Thorel, who shared a picture of migrants on the rescue boat, wrapped in survival blankets, said no one died on the boat she was involved with rescuing.

French Prime Minister Elisabeth Borne said junior Maritime Affairs Minister Herve Berville would head to Calais, near where one of the migrant boats capsized. "My thoughts are with the victims," she posted on messaging platform X.

Britain's coastguard said it sent a lifeboat from Dover to assist with the rescue, along with a coastguard rescue team and ambulance staff.

A UK Border Force vessel and two lifeboats rescued all those on board another small boat in the Channel in a separate incident on Saturday, the British coastguard added. (Reuters)