The party's secretary general, Nicolas Bay, warned of Macron getting "a majority so big that he will have a sort of blank check for the next five years".
"They agreed that the strong friendship between our two countries was important and would endure", the spokesman said.
Macron was not expected to win an outright majority only a few weeks ago.
France's far-right National Front leader Marine Le Pen is expected to notch up a paltry score in the election.
Voters return to the polls next Sunday for a runoff round that will determine how many seats each party wins in the 577-seat National Assembly.
Victory for Mr Macron's party would be a watershed moment, pushing the two established parties to the sidelines.
She also slammed the electoral system as unfavorable to smaller parties like hers.
The Republicans are projected to have taken 20.9% of the vote, which is predicted to result in the party winning between 80-100 seats.
French voters are choosing MPs on Sunday in a vote that is crucial for newly-elected president Emmanuel Macron - but turnout is at a record low.
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Asked if he was anxious about de Villiers, coach Russell Domingo said: "No, not at all". If you took wickets, every good team feels under pressure".
The party has already come first in 10 of the 11 French overseas constituencies that voted before the mainland.
The far-left France Insoumise (France Unbowed) party of Jean-Luc Melenchon is also hoping to perform strongly and inflict more pain on the Socialists.
Polling agencies project that Macron's party will win a large majority in the second round June 18.
The final results will be confirmed next Sunday after the second round of voting.
To win a seat in the first round of voting, candidates need to win more than half of the votes which must account for at least a quarter of the registered voters.
Both the centre-right Republicans and the Socialists failed to reach the presidential run-off last month, for the first time in France's post-war history.
The government has announced legislation to clean up corruption and nepotism in politics, a major reform of worker protections, a bill to extend the state of emergency until November and another one to introduce permanent security measures.
It is the first test of support for Macron and his En Marche party since he swept to power in the presidential election in May. Interior Ministry data showed 40.75 per cent of registered voters had cast ballots by 4pm United Kingdom time, well below the 48.31 per cent at the same time in the 2012 election.
Some 7,882 candidates will be competing for the lower house of parliament's 577 seats.
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