Two French citizens were among the seven people killed in the London Bridge attack, the country's foreign ministry said.
A third French national was still missing and four were gravely injured, the statement added.
Le Parisien daily newspaper named the dead man as 36-year-old Sebastian Belanger.
Police said they feared a French tourist, 45-year-old Xavier Thomas, had been thrown into the River Thames by the attackers' van and drowned.
His girlfriend was seriously injured in the collision.
It comes after a man was arrested on suspicion of terror offences after an early morning raid at an address in east London.
The 30-year-old was held on suspicion of the commission, preparation or instigation of terrorist acts during a search of a property in Ilford and taken for questioning at a south London police station, Scotland Yard said.
Detectives also arrested a 27-year-old man under the Terrorism Act at an address in Barking, east London, shortly after 8am on Tuesday.
On Tuesday the third attacker was named as Youssef Zaghba, an Italian national of Moroccan descent, who was living in east London.
Zaghba, Pakistan-born British citizen Khuram Butt, 27, and Rachid Redouane, 30, who claimed to be Moroccan-Libyan, launched a murderous rampage around London Bridge and Borough Market on Saturday night.
Police shot and killed the three perpetrators within eight minutes of the alarm being raised, but 48 people had already been injured.
Additional reporting by agencies
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