Xavier Thomas, 45, is thought to have been struck by the terrorists' van on the bridge and witnesses reported him being thrown into the water.
British police hunting for a Frenchman missing since Saturday's attack said earlier that they had found a body in the River Thames.
In a statement, police said: "Formal identification has not yet taken place, however Mr Thomas' next of kin have been informed of this development".
French President Emmanuel Macron said a third French victim had been identified among those killed in the attack, adding: "We are paying a heavy cost in these attacks".
The arrest comes as security services face growing questions over their monitoring of the three attackers in the lead up to the attack.
Italian officials said suspicions about him had been shared with British authorities. After a period living together in Morocco, Zaghba's parents separated and the mother returned to Italy.
Zaghba, 22, has been identified as the third of the three attackers shot dead by police after their attack in London on Saturday that killed seven people and left dozens injured.More news: Climate deal pull-out may speed up damage to Trump property
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British police arrested a man under counter terrorism laws on Wednesday as part of an investigation into the London Bridge attack.
Butt was previously known to the authorities, even appearing a Channel 4 documentary about British-based Islamists titled 'The Jihadis Next Door' in 2016.
Libyan security sources also revealed that Redouane, had fought in the revolution against Muammar Gaddafi and joined a militia brigade that went on to send foreign fighters to Syria.
"The security and intelligence services and police have stopped 18 plots since 2013, including five since the Westminster attack two months ago".
Although Khuram B. was known to authorities, police on Monday said, "There was no intelligence to suggest that this attack was being planned and the investigation had been prioritized accordingly".
Police also confirmed there was a call about him to an anti-terrorism hotline, but no evidence was given that he was planning an attack.
The first man, 27, was detained on suspicion of the preparation of terrorist acts, while the second, 33, was arrested on suspicion of possession with intent to supply controlled drugs.
An eyewitness said it was not long before they had completed a loop of the market and came back to Cafe Brood before continuing onto the Black and Blue restaurant where they were finally gunned down by police.