In what is Britain's deadliest terror attack in 12 years, police said a man detonated a bomb at a concert in the northwest English city by US pop star Ariana Grande.
Children were among those killed, police have said, in what May called an “appalling terrorist attack”.
French President Emmanuel Macron voiced his “horror” at the attack that killed 22 people and said he plans to speak to British Prime Minister Theresa May.
On Tuesday afternoon Macron signed the book of condolences for the attack at the British Embassy in Paris, as reported by France 24 (see below).
Macron “learnt with horror and shock about the attack that occurred on Monday evening,” his office said in a statement.
“He addresses all of France's compassion and concern to the people of Britain and stands by its side in this period of mourning, with a particular thought for the victims and their families,” the statement added.
French prime minister Edouard Philippe condemned the attack as “the most cowardly terrorism” that was aimed “specifically and knowingly” at young people.
“I call on my fellow citizens to observe the utmost vigilance, confronted as we are with a threat which is more present than ever,” Philippe said.
Paris mayor Anne Hidalgo has responded to the attacks in a series of tweets, expressing her sympathies in both English and French. Hildalgo also confirmed that concerts would go ahead as planned on Tuesday in Paris. “It is essential to continue to live,” she wrote.
The Paris firemen, who also carry out ambulance duties and were on the front line during the Paris terror attacks, were among those organisations expressing their sympathy in response to the attack in Manchester.
An organisation for the victims of the Paris terror attacks, Life for Paris posted their response on Facebook, saying, “We have just learned of the attacks in Manchester. It is still too early to determine its nature, but we do not consider that to be important — the violence remains the same.”
The statement went on to say: “All our thoughts go to the victims, their families and friends who must be experiencing a painful moment of uncertainty.”
France has been a frequent target of attacks since January 2015 with more than 230 people killed, including 90 in the Bataclan concert hall in Paris during the November 2015 attacks.