The text also prohibits selling or giving away sunbeds to non-professionals, and is part of a wider health bill expected to be voted into law by year's end.
"Our fellow citizens don't know the risks they're taking... We are worried about the home use of these machines," said Health Minister Marisol Touraine.
The bill also introduces requirements that tanning salon staff receive proper training on the health risks of UV ray exposure.
Socialist legislator and former skin cancer specialist Michele Delaunay said tanning-induced melanoma is the second-fastest-growing form of cancer, after lung cancer among women.
"The number of skin cancer cases is doubling every ten years," Delaunay said, adding that experts have substantiated health risks involved to UV ray exposure in sunbeds.
There are some 10,700 tanning salons in France, and 40,000 sunbeds.
Brazil and Australia have both banned minors from using tanning salons.
The UN's World Health Organization has warned that "UV radiation plays an important role in the development of skin cancer, cataracts, and other eye conditions, and suppresses the immune system."