The vote ended with 291 votes in favour and 241 against. Prime Minister Sébastien Lecornu will now ask France's Constitutional Council to review the proposal. If it is approved there as well, it will become law.
The controversial proposal was put forward by President Emmanuel Macron, and the issue has divided both the public and politicians for years.
The conservative majority in the upper house, the Senate, has previously rejected the proposal. But the French constitution gives the lower house, the National Assembly, the final say when both chambers of parliament disagree.
Only adults of full mental capacity will be allowed to request assistance in dying, according to the proposal. They need to suffer from an incurable condition that is life-threatening, and whose pain cannot be alleviated or is not considered manageable by the patient.
If a doctor gives their approval, a lethal substance will then be prescribed to the patient, who can administer it themselves or, if that is not possible, get help from a healthcare professional. Patients suffering from psychiatric or neurodegenerative diseases, such as Alzheimer's, will not be able to receive euthanasia.
If the proposal becomes a reality, France will join countries such as the Netherlands, Belgium, Switzerland and Spain that have similar legislation.
