The violence began on Saturday when a man reportedly shouting "Allahu Akbar" was shot dead after walking into a police station in the central town of Joue-les-Tours where he attacked three officers with a knife, two of whom were seriously injured.
Then on Sunday evening, a driver ploughed into pedestrians in Dijon in the east, injuring 13 people and also shouting the same Islamic phrase which means "God Is Greater" and has been used by jihadists waging violent attacks in the past.
On Monday night, another man rammed into a bustling Christmas market with his car in the western city of Nantes, injuring 10 people, one of whom has since been pronounced clinically dead, before stabbing himself repeatedly and being arrested.
On Tuesday Valls stressed that the three incidents were "distinct", urging the French to keep their calm and act with restraint, although he stressed that security would be heightened.
He announced that the number of patrols would be increased during the Christmas and New Year period
200 to 300 soldiers are to be deployed in the coming hours," he said live on television, after holding an emergency meeting with his ministers.
Although the attacks differ widely, they also present disturbing similarities, and while Valls stressed on Tuesday there was no link between the three, the possibility of violence inspired by Islamic extremism cannot be ignored.
In September, the radical Islamic State group that controls swathes of Iraq and Syria urged Muslims around the world to kill "in any manner" those from countries involved in a coalition fighting its jihadists, singling out the French.
Among instructions detailing how to kill civilians or military personnel was to "run him over with your car."
The Burundian convert to Islam who attacked police on Saturday had posted an Islamic State flag on his Facebook page.
The prosecutors in charge of probing the driving incidents in Dijon and Nantes both insisted they were not "terrorist acts".
The assailant in Dijon, had been to psychiatric hospitals 157 times, local prosecutor Marie-Christine Tarrare told reporters.
She said he told police that he ploughed into people due to a sudden "outburst of empathy for the children of Chechnya" and had shouted "Allahu Akbar" to give him courage.
Interior Minister Bernard Cazeneuve meanwhile said the attacker in Nantes also appeared to be "unbalanced" and not motivated by politics or religion.
But the government faced criticism on Tuesday that it was minimising the threat, at a time when more than 1,000 nationals are thought be involved in jihad on home soil, or in Syria and Iraq.
"Fear over Christmas" titled daily Le Parisien, while Le Figaro newspaper wrote a front-page editorial headlined "enemies within."
Saturday's assailant, Bertrand Nzohabonayo, was not on a domestic intelligence watch-list but his brother Brice is well known for his radical views and was arrested in Burundi soon after the incident.
Nzohabonayo's mother had also told authorities that she was worried about Brice's radicalisation and "the influence he could have on his brother Bertrand," said Paris prosecutor Francois Molins, whose office is in charge of the probe.
The assailant in Dijon, meanwhile, had taken an interest in religion and started wearing a djellaba a long robe worn in Muslim countries just a week ago, according to his mother.