The meeting was broadcast on the parliament's website.
The amendment to the country's legislation, put forward by lawmakers of the left-wing France Unbowed party, reads that the law guarantees legal access and exercise of the right to voluntary termination of pregnancy.
The statute was supported by 337 lawmakers and opposed by 32.
The amendment still needs to be approved by the Senate, the upper house of the French parliament.
In June, the US Supreme Court overturned the precedent established in the 1973 Roe v. Wade decision and ruled that states may regulate the practice of abortion. In July, the European Parliament said that the right to abortion should be included in the Charter of Fundamental Rights of the European Union.