The overuse of the smart devices and inability to switch off has been blamed for widespread "burn out" and "sleeplessness" among employees.
French workplace expert, Xavier Zunigo, told the Independent the bill is a "protective measure".
"There's a real expectation that companies will seize on the 'right to disconnect' as a protective measure," he said.
"At the same time, workers don't want to lose the autonomy and flexibility that digital devices give them."
French labour minister Myriam El Khomri introduced the bill.
Last year El Khomri commissioned a report warning about the health impact of "info-obesity" which is said to affect many workplaces.
A study conducted last year found more than half of France's managers worked between 8pm and midnight when at home.
The new labour law is aimed at encouraging companies to prevent employees from responded to emails outside of the office and to make the French labour market more flexible.