By William Horsley BBC European affairs analyst

The victory of Jacques Chirac over his far-right rival Jean-Marie Le Pen has shown the clear rejection of the policies of the National Front by a majority of French voters.

With the elevation of Mr Le Pen to sole contender with Mr Chirac for the Elysee Palace, Europe's far right made its single biggest advance in 50 years

Yet Mr Le Pen can claim that the first round vote two weeks ago showed him to be the second most popular politician in France.

The genie is out of the bottle. A taboo has been broken.

The extreme right, with its anti-immigrant and in some cases racist policies, has become more respectable.

Huge advance

Already before last month that had happened in Austria, Italy, Denmark, Belgium and parts of Germany.

With the elevation of Mr Le Pen to sole contender with Mr Chirac for the Elysee Palace, Europe's far right made its single biggest advance in 50 years.

The support that Mr Le Pen won may well lead the next French Government to take a tougher line on crime, immigration and defending French interests in the European Union

Mr Le Pen's campaign has placed the right-wing agenda in the media spotlight.

He ridiculed mainstream political leaders, calling Mr Chirac a liar and a thief.

He promised to restore France's true independence by withdrawing from the European Union and the euro zone, to restore border controls and cut the number of immigrants, to make France for the French.

Although he failed, and even united other parties against him, Mr Le Pen's relative success has made it easier for parties with all or part of that agenda to succeed elsewhere.

Second chance

The National Front has another chance to make itself felt in France's parliamentary elections next month.

The support that Mr Le Pen won may well lead the next French Government to take a tougher line on crime, immigration and defending French interests in the European Union.

French leaders have been taught a lesson in humility - they will have to be less bossy towards the rest of Europe than usual, at least for a time

And those attitudes could prove infectious.

The far right will hope for a boost in forthcoming elections in the Netherlands and Germany.

The Le Pen effect may take other forms, too.

French leaders have been taught a lesson in humility. They will have to be less bossy towards the rest of Europe than usual, at least for a time.

Also, this resurgence of national feeling may impact on the EU's current effort to re-define its own purpose and way of working through a broadly-based European Convention.

The events in France throws doubt on the claim that a full political union would resolve the concerns of European citizens.

The possibility will have to be considered that it would instead lead to a popular revolt on a much bigger scale, and that what European countries need is the flexibility to propose different solutions to problems as they arise in different places.