The "horrifying and deeply tragic incident" will likely mean 2024 is the deadliest year on record for crossings.
Some 37 asylum seekers have lost their lives so far this year, matching the total for 2021.
But with two people missing and more critically ill in hospital, the death toll could rise further, heaping more pressure on the British and French governments to end the Channel crossings crisis.
Olivier Barbarin, the Mayor of Le Portel, near Boulogne-sur-Mer, said the boat was "massively overcrowded" when it set off from a beach in his town early in the morning. The vessel was thought to be carrying about 70 people.
A pregnant woman was among the 12 who died, mayor of Boulogne-surMer Frederic Cuvillier told the BBC.
French interior minister Gerald Darmanin said those killed in the incident included "about 10 women, some of whom were minors".
He added that those killed were "primarily of Eritrean origin", but added that officials "do not have consolidated details that would allow us to specify the exact nationalities".
Rescue
The inflatable reached Cap GrisNez, the headland which is 21 miles away from the UK, and the closest point of France to England, before taking on water.
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