A draft motion states that the National Assembly “invites the French government to use the recognition of the state of Palestine as an instrument to gain a definitive resolution of the conflict".
Like a similar motion passed by the British parliament on 13 October, it will not be binding on the government.
On 30 October Sweden officially recognised the state of Palestine, arousing criticism by Israel and the US.
The Palestinian Authority estimates that 134 countries have recognised the Palestinian state, although the figure is disputed.
On Saturday Europe's foreign policy chief Federica Mogherini called for a Palestinian state sharing Jerusalem as its capital with Israel.
Although the Socialist Party is behind the motion, the government may not act on it immediately.
Foreign Minister Laurent Fabius last week said that France would "obviously at a certain moment” recognise a Palestinian state.
But he added, "The question is when and how? Because this recognition must be useful for efforts to break the deadlock and contribute to a final resolution of the conflict."
France was among 14 EU nations that voted in favour of granting Palestinian territories observer status at the United Nations in November 2012.