The centrist party founded by France's newly elected president Emmanuel Macron, just over a year ago, is projected to win a massive majority in the country's National Assembly after Sunday's first round for voting.
France's Prime Minister, Edouard Philippe, declared victory for the party, saying: "France is back", before promising to go ahead with the party's bold reform agenda.
French polling agencies have said that the upstart political party looks set to win over 400 seats out of 577 in the parliament's lower legislative body. The second round takes place on Sunday 18 June.
Macron's La Republique en March is currently polling first, followed by the centre-right Republicans and then the far-right Front National. The left-wing parties have done less well, with Jean-Luc Melanchon's far-left La France Insoumise coming fourth, though still ahead of former president Francois Hollande's socialist party.
Though the first round election is mired in a historically low turn-out, with just 41% of registered voters casting ballots by late afternoon, Macron's rival in the presidential election's final round, Marine Le Pen's Front National is now projected to only win around 10 seats - a disappointment for a so recently on the edge of the presidency.
Le Pen called the turnout "catastrophic" and urged her supporters to vote in the second round; the Republicans similarly called on their supporters to bring out the vote and ensure a strong opposition against Macron's insurgent party.
Many of La Republique en March's candidates are first timers, with little or no political experience. One junior minister, Mounir Mahjoubi, himself running for a seat in Paris, told the Associated Press that the party's election lead showed that the early days of the Macron presidency had been "exemplary" and that voters wanted to give him a large majority.