The body was found late on Tuesday near London's former dockyards in Limehouse, about two kilometers downstream from London Bridge, where Saturday's attack began.
London police, who have been looking for the body of a French national, have recovered another body from the River Thames.
British police said the formal identification of the body had not yet taken place but that the family of the missing Frenchman, 45-year-old Xavier Thomas, had been informed of the discovery.
"Xavier was in London for the weekend with his girlfriend", the Metropolitan Police said in a statement.
Brittany news outlet Le Telegramme reported an account from Boro Bistro manager Vincent Le Berre, who told how his colleague, Pigeard, was attacked by a terrorist in the bar near Borough Market on Saturday night. Ms Delcros is being treated for severe injuries, but there has been no sign of Mr Thomas.
The current death toll stands at seven people after three assailants wearing fake suicide vests mowed down pedestrians on London Bridge and launched a stabbing spree in bars in nearby Borough Market.
Anyone who has seen him since June 3 or was present on the bridge at the time is asked to ring police on 0800 0961 233.