The attack occurred near to Lake Annecy, in the east of the country on Thursday morning which left all four in a critical condition. Two adults were injured following the attack, one of whom also suffered life-threatening injuries.
Speaking at an OECD ministerial council press conference in France, just hours after the attack, Mr Cleverly said: “Our thoughts are with the victims and the families, and we stand ready to support the French authorities in whichever way we can.
“We have already deployed British consular officials who are travelling to the area to make themselves available to support the family. And of course we stand in strong solidarity with the people of France at this terrible time.”
Speaking to reporters, Line Bonnet-Mathis, the prosecutor of Annecy, cofirmed that two of the children were aged 2, one 3, and another a 22-month-old - one of the children was Dutch.
The suspect, identified as a 31-year-old Syrian asylum-seeker, has been detained by police.
According to Ms Bonnet-Mathis, the suspect has had refugee status in Sweden for the last 10 years. She added that the motive for the attack is unclear at this time but is not related to terrorism and tha the he had no criminal or psychiatric record.
In an update to its travel advice for France, the Foreign Office said: “On 8 June, there was an attack in Annecy, South East France. Six people, including four children, were injured.
“If you are in the area, follow the advice of local authorities. If you require consular support, call the British Consulate in Paris on +33 (0)1 44 51 31 00.”
Video of the attack showed a man in dark glasses and with a blue scarf covering his head brandishing a knife, as people screamed for help.
He slashed at a man carrying rucksacks who tried to approach him, seemingly trying to stop the attack. Inside the enclosed play park itself, a panicked woman frantically pushed a stroller as the attacker approached, yelling "Help! Help!" and ramming the stroller into the park's barriers in her terror.
French President Emmanuel Macron described the assault as an "attack of absolute cowardice." Of the victims, he said "children and an adult are between life and death."
“The nation is in shock,” Mr Macron tweeted.
Prime Minister Rishi Sunak earlier tweeted: “My thoughts are with all of those affected by the shocking attack in Annecy this morning.
Calling it a “truly cowardly act”, he said: “The UK and France have always stood together against acts of violence, and we do so again today.”