According to a local prosecutor, Pascal Marconville, who spoke to news service AFP, the migrants included a mother and her two children and they claimed to have come from Iraq.
Police continue to look for two individuals whom they suspect of being the people smugglers involved in the incident, according to Mr Marconville.
The claims follow a series of attempted Channel crossings in recent days, which have prompted UK Home Secretary to declare a major incident. Of the total number of attempted crossings, 42% were intercepted by French authorities before they made it to the UK.
On Monday, Mr Javid said patrol vessels will be brought back from overseas to the Channel as part of efforts to stem migrant crossings to UK shores via small boats.
In December, around 230 migrants attempted to cross the Channel but just under half were disrupted by the French authorities and never left the French coast, Mr Javid added.