Two polling firms projected the anti-immigration National Front would get a quarter of Sunday’s votes with high-profile candidates, including Marine Le Pen, coming out comfortably ahead.
“The sovereign people have spoken ... acclaiming they want to take back the reins of their destiny,” Le Pen said in a statement. She called the results “the first step in a long march to liberty.”
Prime Minister Manuel Valls called the “vote more than a news alert.”
“It is a shock, an earthquake,” Valls said in remarks broadcast to the nation after the poll projections were released.
“The moment we are living through is serious, very serious, for France and for Europe,” Valls said.
His governing Socialists were trailing in a humiliating third place as expected, according to the estimates, largely reflecting the deep unpopularity of President Francois Hollande.
The real rivalry was between the far right and the conservatives of former President Nicolas Sarkozy, which was in second place, according to estimates.
The National Front won a record 11 towns in March municipal elections and two seats in French parliamentary voting in 2012.
The party campaigns against immigration, particularly from Muslim countries. It also opposes the European Union and the euro currency, blaming them for France’s high unemployment and social woes.
Ipsos and CSA were among polling firms projecting the National Front would get 25 percent of the vote - and drastically increase their three seats in the European Parliament.
The projections use the same methodology for all voting in France and is based on results from a select number of polling stations.