A search and rescue operation was immediately launched
The main ferry port in Calais was closed for several hours after people were seen trying to swim towards a departing vessel.
A search and rescue operation was immediately launched and several have been taken to hospital.
There are currently more than 5,000 migrants camped out around the French port.
They have become increasingly desperate since French and UK authorities invested millions of euros in enhanced security around the ferry terminal and Eurotunnel rail terminal.
In recent weeks, other migrants have been caught trying to cross the English Channel in small boats, rather than sneak aboard lorries heading on the Calais ferries and trains.
Last weekend, three Iranian migrants were rescued from a small rigid inflatable off the Sussex coast, near Hastings.
Another three Iranians were picked up in the channel a few days before that by a UK Border Force Cutter patrolling the shipping lanes.
And last month, 18 Albanians were rescued from a boat in trouble off the Kent village of Dymchurch. Two British men were also found on board the vessel and have since been charged with people smuggling.
Authorities in the UK and France are on heightened alert for similar attempts and have acknowledged that the extra security at Calais has made many migrants increasingly desperate and willing to risk their lives.
The ferry port at Calais has now re-opened and the French maritime authorities have stepped up harbour patrols.