According to a local prosecutor, the migrants included a mother and her two children and they claimed to have come from Iraq.
The suspects include a mother and her two children and they claimed to have come from Iraq, according to prosecutor Pascal Marconville, who spoke to the AFP news service.
Police continue to look for two individuals whom they believe were 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 the UK Home Secretary Sajid Javid to declare a "major incident".
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.
The latest crossing over the festive period saw 12 Iranians - including a child - land on a beach at Lydd-on-Sea, Kent, at 6am on New Year's Eve.
Home Office figures show 539 migrants have attempted to travel to the UK on small boats this year, with around 80% making their attempts in the last three months of 2018.
Of the total number of attempted crossings, 42% were intercepted by French authorities before they made it to the UK.
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.