Socialist MPs had introduced the amendment to the budget for 2016, saying that as "basic needs," tampons, towels and menstrual cups should be taxed at the lower rate.
But the proposal was rejected in the early hours of Thursday morning.
The government opposed the change, saying it would reduce tax receipts in 2016 by 55m euros (Â£40m, $63m).
The feminist collective behind the proposal, Georgette Sand, said it "saw red" at the outcome.
It said the rejection was inevitable given the timing of the vote, and women's under-representation in the chamber.
France's Secretary of State for the Budget, Christian Eckert, said that VAT was also paid at 20% on men's shaving foam - and that the debate was "passionate" but "not simple".
The vote in the National Assembly drew ire from many commentators on social media - with #taxetampon trending in Paris on Thursday.
Many people used red blood as a metaphor for their anger - L'etagere tweeted this image, saying "when you read that for the 75% male MPs feminine protection products are not basic needs":
"You have to ask who is pulling the strings at the National Assembly," tweeted @supermegadrivin.
"If you have your period, you pay for it, physically, socially and financially," tweeted @Menstrues.
The parallel drawn between shaving foam and menstrual products was particularly criticised:
If you want, Christian Eckert, I can go out for a month without a tampon, and you without shaving, and we'll see what happens, tweeted @BoumBoumTcha:
French MPs have voted against an amendment which would have cut VAT paid on sanitary products from 20% to 5.5%.