After a heated debate and protests at the weekend, the National Assembly approved the proposal late on Tuesday night.
It will allow women to obtain an abortion at up to 12 weeks into a pregnacy and punish anyone trying to prevent people going to places where they can receive information about abortion.
The state health service began covering abortion costs about a year ago.
Government spokesperson and Womens' Rights Minister Najat Vallaud-Belkacem told the National Assembly that "abortion is a right in itself and not something that is allowed subject to conditions".
The opposition is split on the measure and protests against it, backed by hard-line Catholics and anti-gay activists, have mobilised fewer people than last year's demonstrations against gay marriage.
During the parliamentary debate Jean-Louis Borloo, the leader of the centre-right UDI party, said the new bill had "created an avoidable rift in our society and a source of tensions and divisions" and former prime minister Francois Fillon claimed that the amendment amounted to a "moral and political fault".
The changes are largely symbolic, since France records about 220,000 abortions a year and one in three French women are estimated to have an abortion during her lifetime.
Other gender-equality measures in the pipeline include extending paternity leave to six months, banning beauty contests for under-13-year-olds and higher fines for failing to achieve gender parity in business and politics.