"We noted the presence of 800 to 1,000 migrants" near the tunnel, a local official told AFP, as a police source described the numbers as "unprecedented" for daytime.
People normally try to cross over under cover of darkness, often having paid exorbitant sums to smugglers to make dangerous, even life-threatening bids to reach the other side of the Channel.
"As they approached the tunnel, several migrants tried hard to slow down the flow of traffic so they could climb into the trucks," the source said.
An AFP journalist saw young men climb on top of trucks heading towards Britain, with some cutting through the tarpaulin covering the vehicles to get inside.
Others could be seen helping their friends climb into the back of a white truck.
Several people succeeded in their bid to enter the Channel Tunnel site, the journalist said.
"Security forces were deployed... objects were being thrown at them, and they had to resort to using tear gas," police said in a statement.
Some 4,500 people fleeing war and poverty in Asia, the Middle East and Africa live in notoriously squalid conditions in a makeshift camp in Calais known as the "Jungle".
Most of them live in small tents with precious few possessions, braving cold weather conditions as they bide their time before trying to cross the Channel.
Thursday's attempt came after several weeks when only a tiny number of people managed to get through.
Many of the refugees and migrants want to reach Britain because they speak English, or because they have relatives there.
Others simply believe their chances at a better life are higher in Britain.
Earlier this month a 16-year-old Sudanese boy was hit by a van on a motorway close to the Channel Tunnel, becoming the 18th person to die trying to reach Britain from Calais since June.
With security tight around the Calais Jungle, authorities in Belgium said this week that a growing number of migrants are seeking to leave for Britain from the port of Zeebrugge, located some 130 kilometres (80 miles) north of Calais.