Four toddlers and two pensioners were stabbed in a knife attack in the tranquil French mountain town of Annecy on Thursday and the government said the suspected assailant was a Syrian refugee.

A video of the attack, taken by a bystander and verified by Reuters, showed the assailant jump a low wall into a children's playground and repeatedly lunge at a child in a stroller, pushing aside a woman who tries to fend him off.

Two of the wounded children and one adult were in hospital in a life-threatening condition, while the other victims were less seriously hurt.

Prime Minister Elisabeth Borne said the suspected attacker, who was in police custody, was a 31-year old Syrian national who was granted asylum in Sweden 10 years ago. He had entered France legally, she said, and was carrying Swedish identity documents and a Swedish driving license.

Interior Minister Gerald Darmanin said France had rejected an asylum request made by the suspect earlier this month, and that he had been carrying "certain Christian religious insignia."

The local prosecutor leading the investigation said there was no indication that terrorism was the assailant's motivation. The suspect was under investigation for attempted murder.

The four children were just toddlers, aged between 22 months and three years, Annecy prosecutor Line Bonnet-Mathis told reporters.

One of them was a British national, another was Dutch, Bonnet-Mathis said.

As the assailant, who wore a blue-chequered headscarf and sunglasses, slashed at his victims, one bystander tried to stop him by throwing his backpack at him, the video showed.

Police have not publicly released the suspect's name.

A woman identified as his ex-wife told BFM TV that her former partner was a Christian.

"He does not call me for four months. (Our relationship) stopped because we lived in Sweden and he did not want to live in Sweden anymore," she told BFM TV, adding that he had not previously shown a violent streak.

French news agency AFP reported the assailant was carrying a prayer book on his person when he launched his attack.