Here are some facts about the election and what comes next.
HOW DOES THE VOTE WORK?
A total of 577 constituencies are being decided in the election, one for each seat in the National Assembly, the lower house of parliament.
Seventy-six lawmakers were elected in the first round last Sunday - including 39 representing the far-right National Rally (RN) and its allies - leaving 501 seats up for grabs in the run-off.
This Sunday's voting ends at 6 p.m. (1600 GMT) in towns and small cities and 8 p.m. (1800 GMT) in big cities. At 8 p.m., pollsters will issue initial nationwide projections based on early partial results from polling stations that closed earlier in the day. These are usually reliable.
Vote counting is usually fast. However, if the result is tight - for example the RN is within a few seats of an absolute majority - the final result may not be known until the early hours of Monday.
WHO WILL WIN?
The RN topped the first round with a third of the total vote. Opinion polls forecast it will win more seats than any other party but that its margin of victory is shrinking and that it will likely fall short of a working majority.
The left-wing New Popular Front and an alliance of centrist parties supporting President Emmanuel Macron have withdrawn more than 200 candidates from second-round contests to bolster the chances of the front-running anti-RN contender in their districts.
Historically, a more fragmented field has favoured the far right, and the very latest polls - carried out after the candidate withdrawals - suggest the strategy is working and the most likely scenario is a hung parliament, with the far right missing out on an absolute majority.
That outcome would lead to the most political uncertainty.
WHAT TO WATCH?
One key question is whether voters will back the anti-RN candidate in their constituency, or if they choose to abstain or back the far right despite their preferred candidate's recommendations to the contrary.
The RN and its allies will need to win 289 seats to secure an absolute majority and be able to implement their anti-immigration, eurosceptic agenda. The party has said its leader, Jordan Bardella, would be its candidate for prime minister.
In this scenario, Macron's prime minister, Gabriel Attal, would resign immediately. Macron would name a new prime minister who would then be tasked with forming a government. Macron would have the right to veto a nomination if he deemed the person unfit for the role.
The RN has nuanced its stance on what it would do if it finished just shy of an absolute majority. Bardella had said he would not lead an unstable minority government, but the RN's Marine Le Pen has opened the door to courting other lawmakers if it is only lacking a small number of seats.
WHAT IF THE OUTCOME IS A HUNG PARLIAMENT?
Attal has said the mainstream right, left and centrist parties could form ad hoc alliances to vote through individual pieces of legislation in the new parliament, rather than try to put together a coalition government.
On the left, however, some have touted the idea of forming a ruling coalition. Unlike Germany and many other European countries, France has never had a broad coalition government in its modern political history.
Either scenario would be likely to bring political uncertainty and slow down reforms.
WHAT HAPPENS IF THERE IS NO DEAL?
It is possible that none of the three groups - the far right, Macron's centrist alliance or the left - will be big enough to govern alone, reach a coalition deal or provide the assurance it can run a viable minority government.
In such a case, France would risk political paralysis, with little or no legislation being adopted and a caretaker government running basic daily affairs.
COULD MACRON RESIGN?
Macron has hitherto ruled this out, but it might become more appealing to him if policy paralysis prevails. Neither parliament nor the government can force a president to resign.
WHAT WON'T HAPPEN UNDER ANY SCENARIO?
The constitution says there can be no new parliamentary election for another year, so an immediate repeat vote is not an option.
