London police announced Thursday that they had arrested eight people in connection with the attack, which led to the fatal stabbing of a police officer and four others dead before the assailant was shot and killed.
A spokesman for the French foreign ministry confirmed that the three injured pupils are from the Saint-Joseph high school in Concarneau, Brittany.
French President Francois Hollande offered support for Britain and the investigation.
"France, which has been hit so hard in recent times, knows what the British people are suffering today", he said.
Paris Mayor Anne Hidalgo ordered the lights of the Eiffel Tower to be switched off at midnight in homage to the victims of the attack. "We will continue to work together with the United Kingdom and all our allies to show the world that freedom and democracy will always triumph".
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Banks are supposed to confidentially alert authorities to transactions that may warrant further investigation. Coutts has previously been fined in the United Kingdom for violating money laundering rules.
Eyewitnesses described how the attacker deliberately mounted the pavement with a vehicle on Westminster Bridge before hitting more than 12 people - including three police officers returning from a commendation ceremony.
Hidalgo had earlier expressed her "solidarity" in a message to her London counterpart Sadiq Khan, adding: "Paris and London have very close links which have become stronger in the last few decades".
She said the two cities "share the same love of freedom and a commitment to democracy".
After a deadly terrorist attack outside of the U.K. Parliament on Wednesday, landmarks across the world showed their solidarity to the victims.