Five of the migrants were suffering from hypothermia.
French gendarmes picked up the group 15 nautical miles (28 kilometres) northwest of Calais in the early hours after several ships raised the alarm.
Authorities on both sides of the Channel are worried about a sharp increase in the number of migrants attempting to reach Britain by sea since November.
British authorities took in 43 people picked up in English waters on Christmas and the following day alone.
The risk of collisions in one of the world's busiest shipping lanes, as well as strong currents, high winds and the winter cold, make the crossing extremely dangerous.
For years, thousands of migrants from Africa, the Middle East and Asia have attempted to reach Britain from France, mainly by trying to stow away on trucks crossing the Channel.
Officials have been scrambling to understand what is behind the rise in sea crossings.
Some have suggested Britain's exit from the European Union next March could have prompted fears among migrants that border controls could become even
tougher after Brexit.
But aid workers say they doubt the change is motivated by a close following of European politics.
Fabien Sudry, the top security official in the Pas-de-Calais region, told AFP this month that he believed the most likely reason is the arrival of larger-than-usual numbers of Iranians.
That has led to new people-smuggling networks operating off the northern French coast, he said.