"The rhib (rigid-hulled inflatable boat), with 19 people on board was located at 2.00am (0100 GMT) and the incident handed over to Border Force," it said in a statement.
The mission included the deployment of a search and rescue helicopter and lifeboats from Dungeness and Littlestone, coastal towns in Kent, south east England.
Calais coastguard organisation SNSM assisted in the operation, according to its president Bernard Barron.
"We were called for help... With a boat carrying about twenty people between Calais and Dover," he told AFP.
"This confirms our fears: the smugglers are willing to take extreme measures, but the Channel is a real highway, presenting a great danger for this type of crossing," he said.
Four Iranian migrants making a rare attempt to reach Britain by boat from France in February were rescued just in time after their vessel took on water and was close to capsizing.
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