Audio acquired by the Daily Mail reveals HMC Valiant, a Border Force vessel, asked the Athos for permission to enter French waters to collect a migrant boat.
This was granted by the Athos which said: “You can do. It will be most simple for everybody. Thank you.”
When the British vessel asked about the legality Athos replied: “We give you legality to do this, no problem.”
HMC Valiant then crossed into French waters before deploying an inflatable boat to pick up the migrants.
The UK had been urging France to stop migrant boats leaving its waters.
French authorities say they will only intervene if a migrant vessel requests help.
More than 4,300 migrants have reached the UK by boat thus far this year, including over 1,000 in the past week alone.
Home Office figures show 144 migrants reached UK shores on May 29.
It is unclear how many of these were picked up by HMC Valiant.
Speaking to the Daily Mail the sailor who recorded the radio exchange said: “We know the French are escorting migrant boats towards the UK instead of turning them back to France.
“But this is a first time I have heard of British Border Force collecting migrants on the French side of the Channel.
“I have suspected it going on for some time, but the radio message that I happened to overhear on an public channel proves it.
“The French patrol boat captain makes clear the migrants are not in peril at sea.
“They were travelling slowly towards the UK where they would have been collected by UK Border Force vessels in English waters.”
Separately on Friday morning French police cleared several hundred migrants from a camp close to Calais.
It followed an incident earlier this week where dozens of migrants, some armed with axes and golf clubs, stormed into the port.
One French police officer was seriously inquired according to local media reports.