The outcome of the two-round election, which will wrap up on July 7, could impact European financial markets, Western support for Ukraine, and how France's nuclear arsenal and global military force are managed.
Many French voters are frustrated about inflation and economic concerns, as well as President Emmanuel Macron's leadership, which they see as arrogant and out-of-touch with their lives.
Marine Le Pen's anti-immigration National Rally party has tapped and fuelled that discontent, notably via online platforms like TikTok, and dominated all pre-election opinion polls.
A new coalition on the left, the New Popular Front, is also posing a challenge to the pro-business Macron and his centrist alliance Together for the Republic.
There are 49.5 million registered voters who will choose 577 members of the National Assembly, France's influential lower house of parliament, during the two-round voting.
Turnout at midday (8pm AEST) at the first round stood at 25.9 per cent according to interior ministry figures, which is higher from the 2022 legislative elections at this time of the day. It was 18.43 per cent at midday two years ago.
Macron voted in a Paris voting station along with his wife, Brigitte Macron. Earlier, Marine Le Pen, leader of France's resurgent National Rally, cast her ballot in her party's stronghold in northern France.
The vote takes place during the traditional first week of summer vacation in France, and absentee ballot requests were at least five times higher than in the 2022 elections.
After a blitz campaign marred by rising hate speech, voting began early in France's overseas territories, and polling stations opened in mainland France at 8am on (4pm AEST) on Sunday.
The first polling projections are expected at 8pm (4am on Monday AEST), when the final polling stations close, and early official results are expected later on Sunday night (Monday morning AEST).
The voting is taking place during the traditional first week of summer vacation in the country, and absentee ballot requests were at least five times higher than in the 2022 elections, according to figures from the interior ministry.
Voters who turned out in person at a Paris polling station on Sunday had issues from immigration to inflation and the rising cost of living on their minds as the country has grown more divided between the far right and far left blocs with a deeply unpopular and weakened president in the political centre.
"People don't like what has been happening," said Cynthia Justine, a 44-year-old voter in Paris.
"People feel they've lost a lot in recent years. People are angry. I am angry."
She added that with "the rising hate speech", it was necessary for people to express their frustrations with those holding and seeking power and cast their ballots.
"It is important for me because I am a woman and we haven't always had the right to vote," Justine said.
"Because I am a Black woman, it's even more important. A lot is at stake on this day."
Pierre Leclaer, a 78-year-old retiree, said he cast his ballot for the simple reason of "trying to avoid the worst", which for him is "a government that is from the far right, populist, not liberal and not very Republican".
Macron called the early election after his party was trounced in the European Parliament election earlier in June by the National Rally, which has historic ties to racism and antisemitism and is hostile toward France's Muslim community.
It was an audacious gamble that French voters who were complacent about the European Union election would be jolted into turning out for moderate forces in a national election to keep the far right out of power.
Instead, pre-election polls suggest that the National Rally is gaining support and has a chance at winning a parliamentary majority. In that scenario, Macron would be expected to name 28-year-old National Rally President Jordan Bardella as prime minister in an awkward power-sharing system known as "cohabitation".
In the restive French Pacific territory of New Caledonia, polls already closed at 5pm (4pm AEST) due to an 8pm-to-6am curfew that authorities on the archipelago have extended until July 8.
Violence flared on May 13, leaving nine people dead after two weeks of unrest, due to attempts by Macron's government to amend the French Constitution and change voting lists in New Caledonia, which the Indigenous Kanaks feared would further marginalise them. They have long sought to break free from France, which first took the Pacific territory in 1853.
Voters in France's other overseas territories from Saint-Pierre-et-Miquelon, Saint-Barthélemy, Saint-Martin, Guadeloupe, Martinique, Guyana, French Polynesia and those voting in offices opened by embassies and consular posts across the Americas cast their ballots on Saturday.
While Macron has said he won't step down before his presidential term expires in 2027, cohabitation would weaken him at home and on the world stage.
The results of the first round will give a picture of overall voter sentiment, but not necessarily of the overall makeup of the next National Assembly. Predictions are extremely difficult because of the complicated voting system, and because parties will work between the two rounds to make alliances in some constituencies or pull out of others.
In the past, such tactical manoeuvres helped keep far-right candidates from power. But now support for Le Pen's party has spread deep and wide.
Bardella, who has no governing experience, says he would use the powers of prime minister to stop Macron from continuing to supply long-range weapons to Ukraine for the war with Russia. His party has historical ties to Russia.
The party has also questioned the right to citizenship for people born in France, and wants to curtail the rights of French citizens with dual nationality. Critics say this undermines fundamental human rights and is a threat to France's democratic ideals.
Meanwhile, huge public spending promises by the National Rally and especially the left-wing coalition have shaken markets and ignited worries about France's heavy debt, already criticised by EU watchdogs.
