France's Interior Minister Bruno Retailleau deplored a "terrible tragedy" on X, saying that the child "was trampled to death in a boat".
"The smugglers have the blood of these people on their hands," Retailleau added, saying his newly-appointed government is to "intensify the fight against these mafias who make money from these deadly crossings".
Saturday's deaths come as a series of shipwrecks made 2024 the deadliest in recent years on the English Channel.
Last month, 12 people died after a boat carrying migrants ripped apart in the English Channel.
About two weeks later, eight migrants died in a similar crossing attempt.
In a news conference, the prefect of the Pas-de-Calais, Jacques Billant, said rescuers found the two-year-old child dead onboard a migrant boat that had called for assistance on Saturday morning.
Aujourd'hui plusieurs personnes ont péri en tentant de traverser la Manche. Un enfant est mort piétiné dans une embarcation. Épouvantable drame qui doit tous nous faire prendre conscience de la tragédie qui se joue. Les passeurs ont le sang de ces personnes sur les mains et notre…— Bruno Retailleau (@BrunoRetailleau) October 5, 2024
Fourteen other migrants picked up on board the rescue boat were brought back to France to be interviewed by the border police and a 17-year-old was brought to a hospital in the port city of Boulogne-sur-Mer as he suffered from burns to his legs, Billant said.
Other people on the migrant boat who refused to be rescued continued their journey toward the UK, he said.
"To make money and with no regard for human life, networks of smugglers put people at ever greater risk," including families with children "literally leading them to accident and death," Billant said.
Boulogne-sur-Mer prosecutor Guirec Le Bras said the child, who appears to have been crushed in a jostling on the boat, was born in Germany from a 24-year-old Somalian mother.
In a separate incident, Billant said rescuers found three migrants dead and saved several others as they fell off a small boat overloaded with 83 passengers amid "panic and stampede".
Those dead "were probably crushed" and "have choked ... and drowned in the 40cm of water at the bottom of the inflatable boat," he said.
They were two men and a woman, the three of them aged about 30, he said.
Migrants that rescuers took care of on Saturday came from Eritrea, Vietnam, Afghanistan, Iran, Ethiopia, Libya, Syria, Egypt, Kuwait and Iraq, Billant said.
The prosecutor said investigations have been open on both incidents.
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