Voters dramatically altered the make-up of the European Parliament by doubling the number of MEPs from the populist, eurosceptic right and the anti-austerity left.
Without waiting for the final result, French Prime Minister Manuel Valls went on television to call the result "an earthquake" for France and Europe, and senior minister Segolene Royal acknowledged that the far right's success represented "a shock on a global scale."
The far-right National Front topped the polls in the elections, as average results from five polling institutes pointed to the anti-immigration, anti-EU party led by Marine Le Pen taking 24-25% of the popular vote and around a third – between 23 and 25 – of France's 74 seats in the European Parliament.
The mainstream right Union for a Popular Movement was beaten into second place with a projected 20-21% score and the ruling Socialist Party was left in third place with just 14-15%.
Far-right and hard-left parties gained ground in many other countries, too, including Greece, where the extreme right Golden Dawn are thought to have won nearly 10% of the vote.
The center-right parties were expected to be the biggest group, with 212 out of 751 seats. The Socialists were expected to gain 185 seats, the Liberals third with 71, the Greens fourth with 55 and the far-left next with 45.
Eurosceptic parties were expected to win about 143 seats.
The winners in Greece, the anti-austerity movement Syriza, is thought to have topped the polls with more than 27% of the vote.
In Germany, the EU's biggest member state with the largest number of seats, the pro-European center ground held firm, according to the polls.
The French result is the highest score ever obtained in a nationwide election by the National Front (FN) and follows breakthrough gains made by the once pariah party in municipal elections earlier in the year.
FN leaders celebrated their triumph by demanding the resignation of Socialist President Francois Hollande and the dissolution of France's National Assembly.
Marine Le Pen said voters had demonstrated their desire to "reclaim the reins of their own destiny."
"Our people demand only one type of politics - a politics of the French, for the French and with the French. They have said they no longer want to be ruled from outside, to have to submit to laws they did not vote for or to obey (EU) commissioners who are not subject to the legitimacy of universal suffrage."
The FN's score suggests Le Pen has a real chance of progressing to the final two-candidate run-off when France next votes for its head of state, in 2017.