Socialists have won an absolute majority in Sunday's run-off parliamentary election, according to polling firm estimates obtained by AFP.
The Socialists' parliamentary bloc obtained between 312 and 326 seats -- far more than the 289 seats needed for a majority in the 577-seat National Assembly -- so will not need to rely on support from the Greens or the far left.
The right-wing UMP party of ex-president Nicolas Sarkozy and its allies took between 212 and 234 seats, the Greens took 18 to 24, and the Communist-backed Left Front took nine to 11, according to the estimates from polling firms Sofres and CSA.
The far-right National Front of Marine Le Pen took one to four seats and the centrist MoDem one or two seats.
If confirmed, it would be the first time the anti-immigrant and anti-EU National Front has sat in the Assembly since 1998.
Hollande, who defeated Sarkozy in presidential elections in May, had urged voters to give him the majority he needs to steer France through the eurozone crisis, rising unemployment and a faltering economy.