France is to step up police and military patrols in areas frequented by the public following recent attacks, Prime Minister Manuel Valls has said.
He said up to 300 soldiers would be deployed around the country to boost security over the Christmas period.
The attacks, seemingly unrelated, in Nantes, Dijon and Tours have left more than 20 people injured.
One person injured in Monday's attack on a Christmas market in Nantes has been declared clinically dead.
Nine others were injured in the incident, where a man drove a van towards a stall in the market before repeatedly stabbing himself.
In Dijon on Sunday, a driver shouting "God is great" in Arabic ploughed into pedestrians, injuring 13 people.
On Saturday, a man using the same phrase was shot dead by police after attacking them.
On Tuesday, Mr Valls sought to reassure the public, saying he understood the public's "strong concerns".
President Francois Hollande has called for an emergency cabinet meeting on Tuesday and urged the public not to panic.
The BBC's Hugh Schofield in Paris says French authorities are playing down the idea that there is a pattern behind the three attacks.
However, many people will be asking themselves if there is a copycat element to them, he adds.
Mr Valls told Europe 1 radio there was "no link" between the three attacks and that security forces were dealing with individuals who acted alone.
"We do not minimise these acts," he said, adding that the government wanted to "reassure" the public and understand what had happened.
"The best response is to continue to live peacefully with the necessary vigilance of course," he added.
Separately, police in the southern city of Cannes arrested a man armed with two shotguns and a long knife at a local market on Tuesday morning.
The man's motivations were unclear, but prosecutors did not think that there was any link to terrorism, French media reports said.
Monday's attack in the western city of Nantes took place at about 19:00 local time (18:00 GMT), with witnesses saying the van drove towards a stall selling mulled wine.
Ten people were wounded in the attack. One was clinically dead as a result of their injuries, Mr Hollande said.
French officials say the motive behind the attack is not clear.
"I wouldn't say it was a terrorist attack. I would call it a deliberate act," French interior ministry spokesman Pierre-Henry Brandet said, adding that an investigation was underway.
Interior Minister Bernard Cazeneuve said the attacker in Nantes seemed to be "unbalanced".
Prosecutors made similar comments about Sunday's car attack in Dijon.
The driver was arrested after targeting pedestrians in five different parts of the city in the space of half an hour.
The city's prosecutor said the attacker had a long history of mental illness, and the incident was not linked to terrorism.
Meanwhile, in Saturday's incident, a man stabbed three police officers in the city of Tours before being shot dead.
Anti-terrorism investigators have opened an inquiry into that attack.