In a park by the lake in Annecy, the children – aged around three – were on a morning outing with their minders when a man wielding a knife suddenly appeared and began to stab them, some in their pushchairs.
He ran from the scene and then attacked an elderly man who was walking nearby.
At this point police intervened, and the attacker was shot in the legs and overpowered.
Two children and the elderly man are reported to be in a life-threatening condition in hospital.
Police say the attacker is a Syrian man, aged 45, who was seeking refugee status.
French President Emmanuel Macron has tweeted about the knife attack, calling it an act of “cowardice”.
He says children and an adult are in critical condition, which ties in with the most recent reports by AFP, outlined in our previous post.
“The nation is in shock,” Macron adds.
“Our thoughts are with [those hurt] as well as their families and the emergency services.”
Details are still emerging about the number of people injured and how badly they’re hurt.
News agency AFP is now reporting that, in total, five people are injured including four children.
Two children and an adult are in critical condition, AFP reports, citing an anonymous source with knowledge of the situation.
These numbers haven’t yet been verified and they contradict an earlier report from Reuters that the three people in critical condition were all children.