The proposed bill backed by the Socialist government stops short of recommending lethal injections and avoids the terms euthanasia or assisted suicide.
Prime minister Manuel Valls praised "a reform that proclaims the right to die peacefully, in dignity and without suffering," in a speech at France's lower house of Parliament.
The measure would give people "the right to deep, continuous sedation until death" at the patient's request, but only when their condition is life-threatening in the short term.
The vote is scheduled next week at France's lower house of Parliament. The bill will then be debated by the Senate. The measure has stirred debate in France.
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Five high-profile Christian, Muslim and Jewish leaders on yesterday called for the preservation of "the prohibition of killing" in a joint column published by Le Monde.
Today, about 200 protesters gathered near the lower house of Parliament to denounce the bill as amounting to disguised euthanasia. Another protest by about 200 pro-euthanasia campaigners later criticised the bill as not going far enough.
The method doesn't actively kill patients. But some doctors say it can mean patients are sedated for weeks before they die, and that it may be more humane to euthanize.
The bill specifically mentions that "artificial nutrition and hydration" are considered as medical treatments that could be stopped or not started at the patient's request.
French debate over end-of-life legislation resurfaced last year over the case of comatose Frenchman Vincent Lambert.
His wife wants doctors to stop life support but his parents disagree. The case is pending at the European Court of Human Rights.