“Four French people were injured and it seems one person was particularly affected,” Foreign Minister Jean-Yves Le Drian told France Info radio.
Three men mowed down pedestrians with a van on London Bridge on Saturday before attacking revellers in a popular nightlife hub with knives.
The three were shot dead by police at the scene, while 48 people were rushed to hospital after the attack.
This was Britain's third deadly terror attack since March.
The French anti-terrorism prosecution service said on Sunday it had opened an investigation into the attack, a common procedure when French citizens are among the victims of a terror attack outside France.
Presidential spokesman Christophe Castaner had previously told French radio that “two French people are wounded, one in a serious condition”.
The Elysee Palace said in a separate statement that France was doing everything it could to help the wounded, adding that security would be tightened for expatriates voting in London on Sunday in the upcoming French parliamentary election.
“The attack which struck London… is a new abominable, cowardly attack on our free societies,” the presidency said.
President Emmanuel Macron voiced his support for Britain and said France “will continue to fight terrorism with all its powers, alongside the United Kingdom and all affected countries.”
France has suffered its own wave of terror in recent years, with more than 200 people killed in jihadist attacks since 2015.