The text of the law now goes to the mediation committee, which draws up a final version. The government is hoping for a final passage next Thursday, relying on the votes of conservative Republicans.
Prime Minister Borne said she was convinced there would be a majority to pass the reform. Should the government fail to secure the necessary majority, it could resort to a seldom-used and highly-controversial article of the constitution to pass the law without a vote.
The pension reform provides for an increase in the retirement age from 62 to 64 years. French head of state Emmanuel Macron wants to prevent a deficit in the pension fund, and a majority of French people reject the reform.
There have been strikes and protests in France for weeks because of the project. Hundreds of thousands again protested against the reform on Saturday, although participation was significantly lower than in previous weeks. After the police initially expected up to a million participants nationwide, the government reported only 368,000 demonstrators in the evening. The trade union CGT, on the other hand, put the number of participants at more than one million.
Clashes broke out in the capital Paris, where, according to the Interior Ministry, around 48,000 people demonstrated. Demonstrators threw objects at police officers, shop windows were smashed and several rubbish bins were set on fire. According to the police, 32 people were arrested.
President Macron has been criticized for largely staying out of the pension reform debate. In a letter to the unions published on Thursday, he signaled a willingness to engage in dialogue, but did not respond to the unions' repeated requests to meet with him.