The incident happened near Wimereux at around 2am on Sunday morning.
French paper La Voix du Nord said 72 people, including 10 children, were rescued and taken to Calais while one person was taken to hospital in Boulogne.
The paper said the migrants got into difficulty while trying to board the boat in darkness and cold temperatures.
A Navy helicopter, police and 50 firefighters were involved in the rescue operation.
The Home Office has been approached for comment.
The UK Coastguard could not comment because the incident took place in French territorial waters.
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Published: by Radio NewsHub
Written by: Radio News Hub