It added that men, women and children were on board and that three men were arrested on suspicion of immigration offences.
French authorities said that a fishing boat raised the alarm after spotting the boat off the tip of northern France.
French navy, police and customs deployed a helicopter, a tug boat and three other vessels.
However when they reached the migrants' location, they had crossed over to the British side of the Channel where they were picked up by a British vessel, said the regional authority in northern France.
Some 500 people attempted to cross the Channel to Britain last year, compared with just 13 known attempts in 2017.
In December, a British Royal Navy ship was sent to help coastguard boats watch over the 33 kilometres of sea that separate France and Britain at its narrowest point.
France also responded by announcing broader surveillance measures in early January.