The National Front (FN) won around 25 per cent of the vote, according to exit polls, easily beating the centre-right UMP on 20 per cent while President Francois Hollande's Socialists were humbled with just 15 per cent.
If confirmed, it would be the highest ever national vote garnered by the anti-immigration, anti-EU party led by Marine Le Pen who has promised to shake up the country and the EU.
"It is a historic score. We are now the first party in France," FN vice-president Florian Philippot said as senior Socialist minister Segolene Royal acknowledged that the far-right's victory represented "a shock on a global scale."
In twice-bailed out Greece, Syriza leader Alexis Tsipras has been blunt in his attacks on the cutbacks and reforms demanded by its international creditors, saying they have made the situation worse in a country where more than half of under-25's cannot find a job.
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There was better news for the pro-EU camp in Germany where Chancellor Angela Merkel's conservative party won 36 per cent of the vote, while its coalition partner, the centre-left Social Democrats scored 27.5 per cent.
Exit polls showed anti-EU Alternative for Germany (AfD), founded only last year, with 6.5 per cent of the vote, putting it above the threshold needed to get seats in the European Parliament.
In many countries, anti-euro and anti-immigration parties tapped into growing voter frustration with the EU, saying Brussels has too much power and does not listen.
In Britain, the eurosceptic UK Independence Party (UKIP) led by Nigel Farage -- a party without a single seat in the national parliament -- set the scene Thursday with a major breakthrough in local council polls.
In addition to how the parties fare, a key issue will be the final turnout figures after participation hit a record low 43 per cent in 2009 as voters stayed away in droves.
Early indications suggested slightly higher turnout, notably in France, Germany and Portugal but in Slovakia, the worst performer in 2009, it looked set to be even lower at just 13 per cent.