Hollande's prayer that voters will not tie his hands

If President François Hollande could have a secular prayer before the first round of parliamentary elections in France today, it would be something like this: "Oh God of elections, give me a left-wing majority but, please, not too left."

France's new president has surfed on a wave of popularity since his election on 6 May but the charmed life of "Monsieur Normal" could end abruptly if he fails to win a manageable majority in the new National Assembly in the second round of the legislative elections next Sunday.

All polls suggest that French electors will give the boot to the large, centre-right majority in the lower house of parliament and elect a majority of left-wing deputies. French voters are perverse but not so perverse as to elect a centre-left president one month and a centre-right parliament the next.

The opinion polls suggest that a majority for Mr Hollande's Socialists alone – 289 out 577 seats – is out of reach. He and his Prime Minister, Jean-Marc Ayrault, who is also enjoying stratospheric levels of popularity, hope to assemble a majority of the "wider centre-left", embracing Socialist, radicals and Greens. The bizarre rules of the two-round election make precise forecasting impossible but the final polls suggest that Mr Hollande may be disappointed. He may also have to rely on parliamentary support from the Communists and other hard left deputies, running under the Front de Gauche (Left Front) banner of the anti-austerity, Eurosceptic populist, Jean-Luc Mélenchon.

If so, the balanced but creatively vague Hollande-Ayrault economics and fiscal programme for the next five years could be impossible to push through the national assembly. Mr Hollande has promised growth with fiscal discipline, including ill-defined cuts in the French state apparatus to reduce the budget deficit to zero by 2017. Mr Mélenchon and his supporters oppose almost all cuts in state spending and any cuts in the French welfare state, which is, by some estimations, the most generous in the world.

The second round of the election falls on the same day, next Sunday, as the new general election in Greece. The ailing euro could face a "double whammy" if Greeks vote once again to reject their EU bailout terms and President Hollande fails to win a fiscal-dicipline friendly majority in the National Assembly.

The French parliamentary campaign has generated little excitement. Four election days in three months is overkill even for the politically obsessed French. But the two-round election today and next Sunday may have profound consequences for French politics, beyond the ideological chemistry of the new parliamentary majority.

Marine Le Pen's cosmetically enhanced far-right party, the National Front, hopes for new success today, which could break the fragile mold of party politics on the French right.

Unlike the presidential election, more than two candidates can reach the second round if they take 12.5 per cent of all registered voters in the first. The bizarre dynamics of the two-round election mean that electors could face three-way choices in scores of constituencies next Sunday between left, right and far right. In other constitituencies, there may be two-way battles between the far right and left.

The left-wing parties and Greens have an understanding that only the best-placed left candidate fights the second round. Officially, the main centre-right party, the Union pour un Mouvement Populaire refuses to allow similar deals with the NF to "keep out the left". The UMP also refuses to advise its supporters to vote left in two-way battles with the far right.

But the UMP has been left sharply divided between nationalist-populist and traditional conservative camps by the former president Nicolas Sarkozy's unsuccessful copying of NF policies and language in the presidential campaign. Some UMP local leaders and many voters want local second round deals with the NF. Ms Le Pen hopes that these tensions can be exploited after the election to widen and, re-brand, her movement.

Although the NF is predicted to take 15 per cent of the vote nationwide, it may end up with, at most, two seats or none at all. The complexities of "two round" electoral politics are illustrated by the depressed ex-mining town of Hénin-Beamont in the Pas de Calais, where Ms Le Pen has been involved in a vituperative battle with Mr Mélenchon himself. The polls suggest that Ms Le Pen will top the first-round poll today but that neither of the great populist champions may win the seat.

A local Socialist is forecast by some polls (not all) to pip Mr Mélenchon for second place, forcing him to stand down. The combined left vote should then be sufficient to defeat Ms Le Pen in the second round next week.