* Polls forecast landslide win for President Macron's party
* Parliamentary ballot follows Macron's May election win
* Majority key for Macron to carry out pro-business reforms
* Run-off round on June 18 (Adds Belgian state media on exit poll)
PARIS, June 11 (Reuters) - French voters cast their ballots in low numbers on Sunday in the first round of a parliamentary election expected to give President Emmanuel Macron the strong majority needed to carry out the far-reaching economic and social reforms he promises.
The vote to elect the lower house's 577 members comes a month after Macron, a 39-year-old former banker with little political experience, defied the odds to win the presidency of the euro zone's second-largest economy.
If, as polls project, Macron and his fledgling party win a commanding majority in next week's second round, it will be another blow for the mainstream parties on the right and left which failed to get a candidate into the presidential run-off.
"We want a big majority to be able to act and transform France over the next five years," Mounir Mahjoubi, a tech entrepreneur running under Macron's Republic On The Move (LREM) banner told Reuters as he canvassed support in his northern Paris constituency ahead of the vote.
With voting closed in rural areas and towns but still underway in Paris and other big cities, Belgium's public broadcaster RTBF said LREM and centre-right Modem ally had won about 30 percent of votes - in line with opinion polls ahead of the first round.
Citing exit polls but without naming their origin, RTBF said conservative party The Republicans won between 19 and 20 percent, followed by the far-right National Front at 17 percent, hard-left France Unbowed at 12 percent and the Socialist Party at 7-8 percent.
Pollsters have projected that such an outcome would transform into a landslide majority in the second round.
"I think voters are pretty mobilised behind LREM," said Georges Garion, a 64-year-old company manager, before voting began in Paris. "We're seeing a kind of majority cohesion, it's democracy at work."
Across France, however, turnout was low and three pollsters projected it would remain below 50 percent. Interior Ministry data showed 40.75 percent of registered voters had cast ballots by 1500 GMT, well below the 48.31 percent at the same time in the 2012 election.
The weak turnout will likely narrow the second-round field, because candidates need the support of 12.5 percent of registered voters to qualify.
While predicting the outcome can be tricky with 7,882 candidates vying for parliament's seats, even LREM's rivals have been saying they expect Macron to secure a majority.
Their strategy has been to urge voters to make sure the opposition will be big enough to have some clout in parliament. "We shouldn't have a monopolistic party," former prime minister Bernard Cazeneuve, a Socialist, told Reuters.
The survival of the Socialist Party, which ruled France for the past five years but is forecast to get just 15 to 30 seats, is at stake, as is the unity of The Republicans. Some key figures from both parties have rallied behind Macron.
The National Front, reeling from a worse than expected score for chief Marine Le Pen in the presidential election, could miss its target to get enough lawmakers to form a parliamentary group. It is expected though to improve on the two deputies it had in the previous legislature.
In a country with unemployment hovering near 10 percent and at risk of breaking its public deficit commitments, Macron was elected president in May on pledges to overhaul labour rules to make hiring and firing easier, cut corporate tax and invest billions in areas including job training and renewable energy.
Macron also promised to clean up French politics after a string of scandals - a vow already tested by conflict of interest allegations against his former campaign chief Richard Ferrand, as well as reports that centrist ally Francois Bayrou's MoDem party used EU cash to fund Paris staff jobs.
"I thought about voting for Macron but I didn't," said pensioner Jacqueline Laurent after voting in the town of Annecy, close to the Swiss border.
"With Ferrand and Bayrou we could see them falling back into the same old ways, so that was that. I changed my mind."
Polling stations close at 1800 (1600 GMT) in smaller cities and two hours later in Paris and other big cities.
Very few lawmakers are expected to be elected directly in the first round - which requires an outright majority accounting for at least a quarter of registered voters.
With many fresh faces among the candidates, a political landscape divided among many forces from the far-left to the far-right, and abstention predicted to be at just over 50 percent, that is unlikely to happen in many constituencies.
(Additional reporting by Cecile Mantouani, Antoine Boddaert in Paris, and Gabriela Baczynska and Charlotte Steenackers in Brussels; writing by Ingrid Melander; editing by Richard Lough and David Evans)