The French crew and the Portuguese sub spent two hours trying to untangle themselves – around 34 miles off the Lizard.
Those onboard the Daytona did not realise the 220ft Tridente had strayed into their nets, as it took part in a training exercise off the Duchy.
A spokesperson for Portugal’s armed forces said the commander ordered the submarine to surface carefully when he realised that there was a problem.
Nobody was hurt and there was no serious damage.
A spokesperson for French maritime authorities said: “The submarine immediately surfaced and made contact with the trawler.”
The 2,000 tonne submarine headed for Devonport dockyard in Plymouth. It is now understood to have left the base nad is not expected to return.
The Daytona headed back to Brittany, without having to call for help from coastguards or local RNLI crews.