Update - 11.55am: A man flagged by French authorities as a suspected radical has killed his mother and sister and seriously injured another woman in a knife attack that was quickly claimed by Islamic State.
Police shot and killed the man, whose motives were not immediately clear.
Authorities did not rule out a family dispute and prosecutors were not immediately treating the attack as a terrorism case.
Three French officials identified the two people killed in the attack in Trappes as the mother and sister of the attacker.
The third victim, a passer-by who was gravely injured in the attack, was also a woman, one of the officials said.
Police officials said the man was flagged in a government database of suspected religious and political extremists.
The French interior minister said the man had "serious psychiatric problems".
Gerard Collomb said the attack is not being treated as a terrorist case for the moment, despite the claim of responsibility by IS.
The minister said a third person who was seriously injured was not a member of the family.
Mr Collomb said police shot and killed the man after he came out of his mother's house wielding a knife and ignored their warnings.
Update - 10.45am: An attacker has killed two people before being killed by police in a town west of Paris, a senior French official said.
Jean-Jacques Brot, the top government administrator in the Yvelines region, tweeted that the attacker in the town of Trappes was "neutralised" and had died.
[# Trappes] Opération de police achevée
Le RAID n'a pas été engagé. Individu neutralisé et décédé.August 23, 2018
The tweet also said that two of the attacker's victims were killed and another seriously injured.
Earlier, media reports said the attacker had used a knife on his victims before being shot by police.
Islamic State claimed responsibility for the knife attack through its Aamaq news agency in a post shared on social media channels.
The agency said the attack was motivated by calls from the IS leadership to attack civilians in countries at war with the extremist group.
Hours earlier, IS leader Abu Bakr al-Baghdadi urged followers to attack enemies everywhere by all means, including in knife attacks.
A man armed with a knife has attacked passers-by, killing one and seriously injuring two others, before being shot by police west of Paris, reports said.
Police have tweeted that an operation is underway in Trappes, with a security perimeter in place.
BFM-TV reported that the man first sheltered in a house after attacking people before being shot by officers.