Phones are already banned in half of France's schools with politicians hoping the extended ban will cut disruption in classrooms.
It will require pupils in elementary and junior high school to keep their devices in bags or out of sight, in what is being called a "detox measure".
The law, proposed by President Emmanuel Macron's party, is aimed at tackling the increasing use of phones by children in class where they send text messages and communicate on social media.
Around half of the country's 51,000 elementary schools and 7,000 junior high schools already outlaw their use.
According to a 2016 survey, 90% of French students aged between 12 and 17 own a mobile phone.
Education minister Jean-Michel Blanquer described it as "a law for the 21st century, a law for addressing the digital revolution".
"Being open to technologies of the future doesn't mean we have to accept all their uses," he said.
After the bill was passed by the Parliament Mr Blanquer said on Twitter that the new rules would "protect children and teenagers".
The law does not specify any punishment for students who refuse to ditch their phones, and lawyers say French teachers do not have the power to seize non-dangerous items.
It is hoped the law will reduce disruption to lessons, help prevent bullying and improve "camaraderie".
However, critics have suggested that children could still use their phones while pretending to look through their bags.
Hitting back at opponents ahead of the debate, head of Mr Macron's REM party, Richard Ferrand, said the law needed to be combined with a campaign to educate people on the importance of limiting students' phone usage.