The asylum seeker, a man in his 30s, was suffering severe hypothermia despite wearing a wetsuit as he attempted to cross one of the world's busiest shipping lanes.
Crew members on the Dover-bound P&O Pride of Canterbury spotted the "distressed" swimmer at 10.40am on Monday, 11 miles north of Calais, according to The Daily Telegraph.
They launched a small rescue boat to pull him from the water before he was handed over to the French Navy and airlifted to hospital.
Two migrants are known to have died this year trying to cross the Channel, including an Iraqi man who drowned after trying to use plastic bottles as a life jacket, the paper said.
A woman also drowned after falling overboard from a small boat travelling to the UK.
A total of 237 vessels carrying prospective migrants were picked up in the Channel in the first 10 months of 2019, the paper said.