The radical-left France Insoumise (France Unbowed) party of Jean-Luc Melenchon also fell short of expectations.
Socialist Party leader Jean Christophe Cambadelis said the record-low turnout was a "sign of enormous democratic fatigue".
"It's a renewal of the political class", said Jose Jeffrey, a health ministry administrator who voted LREM.
Cambadelis called on voters to favor more political pluralism in the second round.
Analysts say if his party goes to win a landslide victory in the final round on June 18, it will redraw the landscape of French politics.
"France is back", Prime Minister Edouard Philippe said on French TV. That puts it on track to obtain a staggering majority of seats after the election runoff June 18.
The prime minister also thanked security services for protecting voting stations and ensuring a safe vote after a string of deadly extremist attacks.
But Sunday's turnout hit a record low of 49 percent, mirroring the French people's growing disinterest in legislative elections.
(E3) Forza Motorsport 7 pour le 3 octobre
La sortie de Forza Motorsport 7 est prévue pour le 3 octobre et le titre sera disponible sur PC, Xbox One et Xbox One. Cependant, il est certain qu'elle reprendra le moteur 3,8 litres de la Turbo S mais qui sera plus performant.
Parties on the extreme right and left seemed to be faring poorly, gaining far fewer votes nationwide than they had in the first round of the presidential election, on April 23.
If the seat projections are confirmed next week he will have a strong mandate to push through the ambitious labour, economic and social reforms he promised on the campaign trail.
She also slammed the electoral system as unfavourable to smaller parties like hers.
For at least two decades, French unions have opposed such efforts, emphasizing instead job protection for their members, but a week from now, Macron may find himself in a stronger position than any French president for a generation.
Partial official results show that French President Emmanuel Macron's new centrist party is clearly leading the first round of parliamentary elections crucial to his plans to change France.
At the close of voting, pollster Elabe projected Macron's party and its centre-right Modem ally would win 32.6 per cent of the first round vote. The Republicans and their allies fared better, but with just shy of 22 per cent of the vote, they were a distant second to Macron's party. The Republicans would become the largest opposition force with 80-100 seats, Elabe projected, with the National Front seen winning 1 to four seats and the Socialist Party and other leftists 30-40 seats.
Both the Republican and Socialist parties which have traditionally governed during the time of the Fifth Republic, are likely to suffer.
Many voters stayed away from the polls, with turnout of only 50 per cent. Macron's opponents say this helped En Marche - and are now anxious about what the French President could achieve with such a thumping majority.
The low turnout rate in the first round of France's parliamentary election suggests a sharp drop-off in interest among voters after the May election of President Emmanuel Macron. Those talks will get under way in earnest after next Sunday's second-round vote as the government seeks common ground for reworking the country's byzantine labor rules.
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