Marine Le Pen's far-right party was being tipped to emerge as the dominant force in French politics following President Emmanuel Macron's decision to hold a snap poll, Sky News reported.
But the left-wing New Popular Front coalition (NPF) is expected to win the most seats (182) in the second voting round of parliamentary elections.
President Emmanuel Macron's centrist group, Ensemble, is predicted to win 163 seats with National Rally (RN) in third on an estimated 143 seats, according to BFM TV.
After RN emerged from the first round of voting as the leading party, centrist and leftist parties agreed to withdraw 221 candidates, including 83 from President Macron's camp and 132 from the NPF, in order to avoid three-way run-offs.
Le Pen said RN's victory had "merely been delayed", adding that she "sees the seeds of tomorrow's victory in today's result".
She also described Mr Macron's position as "untenable".
Jordan Bardella, president of National Rally, said, "We've been thrown into the arms of the extreme left and of Jean-Luc Melenchon."
He said the coalitions formed in response to RN's success in the first round had "paralyzed" the French political system and Mr. Macron had "pushed the country towards uncertainty and instability".
"I know how many millions of French people must be frustrated," he added.
Mr Macron's office said, "The president, as guarantor of our institutions, will respect the choice of the French people."
It also said he was analyzing the results and waiting for the full picture to emerge.
SD/PR