The proposals are specifically aimed at reducing the high rates of teenage smokers in France.
Health Minister Marisol Touraine plans to follow Australia’s example, which introduced similar measures in 2012.
Experts say removing branding on packets and adding large health warnings reduced smoking in Australia.
However, some tobacco companies dispute the evidence for this and say France’s plans are incomprehensible.
Smoking is the main cause of death in France, with more than 70,000 people dying each year of tobacco-related illnesses.
The new measures, which will come into effect once the law goes through the National Assembly, also includes a ban on smoking in children’s play areas in public parks and in cars carrying children under 12.
In addition, advertising of e-cigarettes will be restricted before being banned in May 2016, except at the point of sale and in trade publications.
Ms Touraine says there are 13 million smokers in France – which has a population of around 66 million – and the “number of smokers is growing, especially among young people.”
“We can’t accept that tobacco kills 73,000 people every year in our country – the equivalent of a plane crash every day with 200 people on board,” she added.
The BBC’s Hugh Schofield in Paris says the move goes well beyond what France is required to do under European anti-smoking rules.