There are 49.5 million registered voters who will choose 577 members of the National Assembly, France’s lower house of parliament, during the two rounds of voting on June 30 and July 7.
Before voting commenced on the mainland, it began in France’s overseas territories.
The first polling projections are expected at 8pm (1900 BST), when the final polling stations close, and early official results are expected later on Sunday night.
In the volatile French Pacific territory of New Caledonia, polls have already closed – at 5pm local time – due to an 8pm-to-6am curfew that authorities on the archipelago have extended until July 8.
If RN does win a majority in the National Assembly, it is expected that Mr Macron will appoint 28-year-old Jordan Bardella.
Bardella, the son of Italian immigrants, has shot to prominence as Marine Le Pen’s sharp-dressed, quick-witted number two.
The young firebrand has millions of social media followers and has previously taken a hard stance on immigration. Should he become the country’s PM, it will significantly weaken President Macron’s position.
In such circumstances, Mr Macron’s remit will be limited when it comes to defence and foreign policy.