The port authorities were alerted when people were seen trying to break into the boat, according to judicial sources.
The 14 migrants said they were from Iraq, among them a mother and her two children.
Police believe two people, possibly the traffickers, escaped when the others were stopped.
There has been a sharp increase in recent months in attempts by migrants to reach Britain by boat.
French and British authorities agreed on Sunday to beef up their attempts to halt the trend.