ANTIQUES SHOPS

A clear majority reliant neither on opposition conservatives nor eurosceptic hard leftists, as opinion polls suggest, would be a boon as Hollande prepares legislation to raise taxes, adjust budget spending and ratify an EU fiscal discipline pact.

Yet with a simultaneous election in Greece threatening to tip Europe into chaos and French voters in no mood for further economic gloom, Hollande will have no time to bask in glory.

Opinion polls and projections from last Sunday's first-round vote suggest the Socialist bloc could achieve the 289 seats needed for a majority in the 577-member National Assembly even without adding seats from its Green Party allies.

Added to its control of the Senate and the presidency, that would give the Socialist Party more power than it has ever held and should leave Hollande's largely social democratic and pro-Europe cabinet broadly intact.

The possible entry of Marine Le Pen's far-right National Front into parliament for the first time since the mid-1980s with up to three seats would be uncomfortable but would not pose any threat to Hollande's power to govern.

"It would probably be better if the Socialists get an absolute majority because they won't be influenced by the far left and they'll be able to govern along more centrist lines," said Yves Collignon, 62, a retired engineer voting in Paris.

Hollande, who won power last month, will fly to Mexico early on Monday with voting slips barely counted for the first of a flurry of summits. His decision to side with southern nations weary of austerity has opened a rift with Europe's paymaster Germany that the Socialist needs to fix fast.

He is toning down calls for joint euro zone bonds - accepting Berlin's insistence this is a long-term prospect - and is instead pushing for a package of growth-boosting measures worth around 120 billion euros.

Hollande may face a challenge keeping eurosceptic Socialist lawmakers behind him if he agrees to Germany's demand for a commitment to deeper fiscal and political integration in Europe.

He may also encounter resistance to slowing down spending plans if a public finance audit due by end-June shows France ill placed to meet its deficit goals, as it is expected to do.

"Hollande's biggest political test will be to keep his party united if he is forced to adopt economic policies that are unpopular with the electorate," political analyst Antonio Barroso of Eurasia Group said in a note to clients.

NO VOTER HONEYMOON

Polling booths opened at 8 a.m. (02.00 a.m. EDT) and the last ones were due to close 12 hours later, with concern over turnout as voters go to the polls for the fourth time in eight weeks. The abstention rate hit a record of nearly 43 percent last Sunday.

Initial results will be released at 8 p.m., the same time the world will learn whether Greece has elected an anti-austerity party whose victory could undermine its euro zone membership and send shockwaves through financial markets.

Hollande's chief ministers, including Prime Minister Jean-Marc Ayrault, were elected in round one by scoring more than 50 percent of votes. Those in run-off contests, like Finance Minister Pierre Moscovici, are expected to win their seats.

In all, 36 deputies were elected outright last weekend and 541 constituencies are up for grabs on Sunday.

A survey by Ipsos-Logica Business Consulting published on Friday, and tallying with other polls, showed Hollande's Socialist bloc could win between 284 and 313 deputies and that the Greens could take 14 to 20 seats.

The radical Left Front coalition, whose leader Jean-Luc Melenchon was knocked out of the running for a seat representing an economically destitute northern town by Le Pen last week, is set to win just 12 to 13 seats.

Le Pen's National Front is looking at up to three seats, and the conservatives, fractured since their leader Nicolas Sarkozy was ousted as president in May, are set for 192 to 226 seats.

The projections are for a bigger parliament win for the left than in the 1997 election, when voters lashed out at the then conservative government's attempt at welfare reform, and in 1988, just after President Francois Mitterrand's re-election.

That would still leave Hollande short of the two-thirds majority he would need for any constitutional changes, such as legislation to give EU institutions more power over the budget.

Hollande faces the risk that opposition lawmakers could demand a referendum in exchange for supporting legislation that many voters would view as undermining French sovereignty.

The fact voters are already marking Hollande harshly suggests they will react angrily if he announces spending cuts.

"My hypothesis is that after the summer there will be social upheaval as people will no longer be able to voice frustration via the ballot box," political expert Dominique Reynie said.

(Additional reporting by Nicholas Vinocur; Editing by Angus MacSwan)

In an election fought over the punishing austerity package demanded by international lenders as the price of keeping Greece from bankruptcy, opinion polls showed the radical leftist SYRIZA party, which wants to scrap the deal, running neck and neck with the conservative New Democracy, which broadly backs it.

The European Union and International Monetary Fund have insisted that the conditions of the 130 billion bailout accord agreed in March must be accepted fully by a new government or funds will be cut off, driving Greece into bankruptcy.

All parties say they will keep Greece in the single currency, but SYRIZA leader Alexis Tsipras believes the agreement can be renegotiated without Greece having to leave, betting that European leaders cannot afford the turmoil that would be unleashed by cutting a member of the euro zone loose.

On the right, establishment heir and New Democracy leader Antonis Samaras says rejection of the EU/IMF bailout would mean a return to the drachma and even greater calamity, although he, too, wants to renegotiate some aspects of the package.

Opinion polls show Greeks, weary after five years of deep recession, overwhelmingly favour remaining in the euro, but there is bitter anger over repeated rounds of tax hikes, slashed spending and sharp cuts in wages.

Many voters are also furious with New Democracy and the other traditional ruling party, the now severely weakened PASOK, blaming them for decades of corruption, waste and inefficiency.

"It's the first time I feel depressed after voting, knowing that I voted again for those who created the problem, but we don't have another choice," said 66-year-old English teacher Koula Louizopoulou.

"I voted for the bailout because these are the terms that will keep us in Europe," she said.

A win for Greece's national soccer team in a game on Saturday at the Euro 2012 championships provided some lift for voters but there was little sign of enthusiasm at the polling booths, which close at 7 p.m. (1600 GMT). Exit polls will follow soon after voting ends.

"STARING INTO THE ABYSS"

"It's obvious the country is now staring into the abyss," leading Greek daily Kathimerini said in a front-page editorial on Sunday, calling for the creation of a New Democracy-led "unity" coalition to keep the country in the euro.

The party gaining the most votes wins an automatic 50-seat advantage but neither New Democracy or SYRIZA is expected to win an outright majority and whoever emerges as top party will have to hold coalition negotiations with smaller groups.

European leaders weighed in on the eve of the vote - a re-run of an earlier election on May 6 that produced no clear winner - some of them openly urging Greeks to reject SYRIZA or risk undermining the very foundations of the single currency.

But whoever wins power may find their tenure is short-lived and, despite the insistence of EU politicians, some adjustment of the bailout terms may be inevitable if Greece is to cut a public debt amounting to 165 percent of gross domestic product.

"It is a scenario I see as likely and if that is the condition presented for Greece to stay and then move on, I would say it is probably something that should be attempted," Angel Gurria, head of the Organization for Economic Cooperation and Development, told Reuters in an interview.

Central banks from Tokyo to London are readying arsenals to defend banks and national currencies against any post-election turmoil. The result will dominate a meeting of the Group of 20 world economic powers on Monday and Tuesday in Mexico.

Finance officials in the euro zone have discussed limiting the size of withdrawals from ATM machines, imposing border checks and introducing euro zone capital controls as a worst-case scenario.

Euro zone officials have hinted they might give a new Greek government some leeway on how it reaches debt targets set by the EU/IMF bailout package, but there would be no change to the targets themselves.

Euro zone paymaster Germany warned Greeks on Saturday the bailout would not be renegotiated.

"That's why it's so important that the Greek elections preferably lead to a result in which those that will form a future government say: 'Yes, we will stick to the agreements'," Chancellor Angela Merkel told a party conference of her Christian Democrats.

A Greek exit from the single currency would heap further pressure on two far larger European economies - Spain has already received up to 100 billion euros to save debt-riddled banks and Italy could be next to seek a bailout.

GERMAN WARNING

Anger with the establishment parties New Democracy and PASOK propelled SYRIZA and its youthful leader, a former Communist student protest organiser, from the obscure radical fringe to a shock second place on May 6.

The far-right Golden Dawn party also won seats in the first election, underscoring the fragmentation of a stressed society wrestling with unemployment of almost 23 percent and plummeting living standards.

Five years of recession and more than two years of acute crisis have started to fray the edges of Greek society, undergoing its severest test since the overthrow of the military dictatorship in 1974.

The streets of central Athens are scarred by repeated waves of protests, some hospitals are short of vital medicines and reports of suicides caused by the crisis have become routine.

Five opinion polls published before a blackout two weeks ago put New Democracy narrowly ahead. Two other polls had SYRIZA leading.

But analysts say Samaras, 61, will find it hard to govern for long with an empowered SYRIZA protesting at the gates. Tsipras, if he wins, will inherit a country on the verge of bankruptcy. He has ruled out a government of national unity and promised to nationalise banks and halt privatisations.

Some global businesses and banks are already in retreat.

Europe's biggest retailer Carrefour said on Friday it was selling up in Greece, a day after French bank Credit Agricole moved to take direct control of its Albanian, Bulgarian and Romanian units from its Greek bank Emporiki.

(Writing by Matt Robinson and James Mackenzie; Editing by Ralph Gowling and Alessandra Rizzo)