The Socialist Party of France's President Francois Hollande has won enough seats in parliament to form an absolute majority, according to polling projections.
The projections suggested the party and its allies would take more than 320 out of 577 seats in the National Assembly.
If confirmed, it would be the Socialists' best result in modern French history.
It gives the president strong backing for his tax-and-spend programme.
He would not have to rely on support in parliament from either the Greens or the far-left.
Mr Hollande has promised to hire more public workers and to refocus EU fiscal efforts away from their emphasis on austerity, and towards growth.
Sunday's vote was the second round of a two-part parliamentary election. Turnout was a record low, at 55.9%.
The projections suggested the conservative UMP party and its allies would win between 212 and 234 seats, and the far-right National Front between two and four seats.
The BBC's Christian Fraser in Paris says it is being reported that the National Front leader, Marine Le Pen, may have been beaten in the northern constituency of Henin-Beaumont; but that her 22-year-old niece, Marion Marechal-Le Pen, won election in Carpentras in the south.
In one of the most closely watched constituencies of La Rochelle, Mr Hollande's ex-partner, the former Socialist presidential contender Segolene Royal, was beaten by a dissident Socialist candidate.
Ms Royal admitted defeat but slammed what she called a "political betrayal".
Earlier in the week Mr Hollande's current partner, Valerie Trierweiler, signalled her support for Ms Royal's opponent, Olivier Falorni - a move seen as highly embarrassing for the president.
Our correspondent said the UMP, the party of the former president Nicolas Sarkozy, had had a miserable campaign which was reflected in the result.
The party currently has no leader.
BBC News, June 17, 2012