The French far-right leader Marine Le Pen narrowly failed to win a parliamentary seat in the Pas de Calais last night, adding to a triumphant day for François Hollande's Socialists.

Two other National Front candidates won seats in the National Assembly for the first time since the mid-1980s. They included Ms Le Pen's 22-year-old niece, Marion Maréchal-Le Pen, who becomes the youngest parliamentarian in French history.

The former Socialist celebrity lawyer, Gilbert Collard, 64, won a seat for the far right in the Rhône delta.

Ms Le Pen saluted an "enormous success" for her party in ending what she called its "illegitimate 25-year absence" from parliament. She suggested that she might bring a formal complaint today about "suspicious" circumstances in her razor-thin, 114-vote defeat in the Pas de Calais by a local Socialist, Philippe Kemel.

Overall, President Hollande's moderate left won a decisive victory in the second round of the parliamentary elections and will have a clear majority to pursue his promised policy of "growth with discipline". His former partner, the 2007 presidential candidate Ségolenè Royal, lost her so-called "tweetgate" battle against a renegade Socialist in La Rochelle.

Official estimates suggested that President Hollande's Socialists would win 313 seats – substantially more than the 289 seats that they need for one-party control of the lower house of parliament. With about 20 Green deputies, far more than ever before, Mr Hollande and his Prime Minister, Jean-Marc Ayrault, should have an overwhelming majority in the 577-seat assembly for the next five years.

President Hollande will be able to pursue his experiment in growth promotion coupled with budgetary discipline, including as yet ill-defined cuts in the sprawling French state.

Since a Hollande victory was almost assured after the first round of voting last weekend, the suspense of France's fourth election night in two months focused on a series of high-profile local races. The xenophobic and anti-European National Front was hoping to break into the assembly for the first time since 1986-88, with a victory for its leader, Marine Le Pen, in the depressed former mining town of Hénin-Beaumont in the Pas de Calais.

Early counting suggested that she had won but the final count put her Socialist rival 114 votes ahead. Election officials refused a recount.

The two victories for the far right elsewhere were hailed by Ms Le Pen as a vindication of her policy of "de-demonising" the NF by excluding overtly racist supporters and language. Tactical manoeuvring between the two rounds of the election breached the barrier between far right and centre right – offering encouragement to Ms Le Pen's plans to redraw the map of party politics.

Mr Collard won a nasty three-way contest, with accusations of violence on all sides, in the "Petite Camargue". In Carpentras, in the Rhône valley, Marion Marechal-Le Pen the grand-daughter of the party's founder, Jean-Marie Le Pen, won a seat in a triangular contest forced by the refusal of a Socialist to withdraw. In Orange, nearby, an independent far-right candidate also won a seat.

Ms Royal failed to save her political career in a two-way fight with a rebel Socialist candidate in La Rochelle on the Atlantic coast. This contest was promoted to the status of global, political soap opera last week by a tweet from the French First Lady, Valérie Trierweiler, publicly encouraging the rebel candidate, Olivier Falorni.

Ms Royal is the mother of the President's four children.