The exit polls suggested Socialist Party and its allies would take more than 312 out of 577 seats in the National Assembly.
If confirmed, it means the Socialists will not have to rely on support from either the Greens or the far-left.
It gives the president strong backing as he seeks measures to boost growth.
Francois Hollande has promised to hire more public workers and to refocus EU fiscal efforts away from their emphasis on austerity.
The vote was the second round of a two-part parliamentary election.
The polls suggested the conservative UMP party and its allies would win between 212 and 234 seats, and the far-right National Front between one and four seats.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…