BRUSSELS (Reuters) - Overshadowed by the prospect of a Socialist win in France'spresidential vote, the parliamentary election in Greece on Sunday carries far greater risks for the euro zone.

Opinion polls show no clear winner emerging from the vote, with the two main parties - centre-right New Democracy and PASOK's socialists - together garnering around 38 percent of the ballot, barely enough for a parliamentary majority under Greece's electoral system.

Either they will secure just enough to work as together, albeit uncomfortably and with a very slim majority, or steps will have to be taken to form a broad coalition with minor parties firmly opposed to theEuropean Union's austerity measures.

That in turn will increase the pressure on the new government to renegotiate parts of the second bailout program, an ambitious deal struck in February that aims to clear the way for Greece to return to financial markets by 2015.

Some economists take the view that Sunday's election could push Greece back to the nadir it touched in November last year, when there was widespread talk of an exit from the euro zone. The contagion effect would drive Spanish and Italian bond yields straight back into the danger zone, economists say.

"Political paralysis in Greece following the elections could lead to a default and even threaten a euro exit, in our view," Bank of America strategist Athanasios Vamvakidis wrote in a research paper published on Tuesday.

"We believe that the troika may have little choice but to stop funding Greece if there is no government in place," he said, referring to the monitoring mission made up of the European Central Bank, the IMFand the European Commission.

PANDORA'S BOX

While others are less apocalyptic, there is a widespread expectation among private-sector analysts that some renegotiation of the second program will be necessary if a balance is to be struck between keeping Greece politically stable and keeping it on track towards debt sustainability.

With French Socialist Francois Hollande expected to lead a charge for the euro zone to put greater emphasis on stimulating growth and to focus less intently on deficit reduction, Greece may be an early candidate for a loosening of its targets.

"A new government is likely to argue for more backloading of the fiscal adjustment to limit the near term economic contraction, and on this issue it is likely to be pushing against an open door," David Mackie, a senior economist at JP Morgan in London, wrote in a note to clients.

That might provide some breathing space for Athens, but it would have implications for Greece's financing and would likely mean that it couldn't return to financial markets in 2015 since a primary budget surplus would remain some way off.

"Thus, a third program seems likely in any event," Mackie said. "The size of that program would have to be larger to the extent that less progress is made on the fiscal side."

The open question is what approach the troika will take. Greece consistently missed targets under its first program, agreed in April 2010, which led to the restructuring of its private-sector debt under the second package.

Officials say any further backsliding now will not be tolerated, especially with the International Monetary Fund a reluctant partner in the second program.

"There is simply no more patience or time for Greece. The only option left for them would be to quit the euro if they don't like the deal they have," said one euro zone official.

"Nobody wants to open Pandora's Box, even in a very small way," he said, referring to a renegotiation of the program.

"Everybody knows that it would mean weeks and weeks of renegotiation and lead to similar and well-justified demands from Ireland and Portugal."

COMPROMISE APPROACH

However, the political reality that emerges from Sunday's vote may force a reassessment, especially if the alternative is a situation in which Greece is nudged closer to euro zone exit, whether in reality or in the mind of the financial markets.

"Even though we believe that a Greek exit from the euro is very unlikely, market speculation about such an event would naturally increase with increased tension between Greece and official lenders," UBS economists Stephane Deo and Justin Knight wrote in a report published on Wednesday.

"Taken further, if the stress rises enough that the idea of a Greek euro exit becomes prevalent beyond financial markets, the risk of further deposit flight - both from Greece and other peripheral member states - would naturally increase."

If the troika stands firm, resisting any calls from the new Greek government to renegotiate the package or soften targets even slightly, then the moment could be forced to its crisis.

With Greek banks recapitalized with up to 50 billion euros of euro zone funds, they are better placed to handle the fallout that would ensue if Greece were to decide to leave the currency union or investors were to bet on such an outcome.

But with euro zone leaders determined that Greece should remain in the currency zone, and polls showing that around 80 percent of Greeks remain committed to the euro, the more likely outcome would still appear to be a compromise between Greece and its official creditors - meaning another debt restructuring.

"Further debt relief is likely to be forthcoming, in the form of a restructuring of official loans," wrote JP Morgan's Mackie, saying that that would likely involve maturity extensions at concessional interest rates.

"Thus, the new Greek government will likely need to commit to some path towards a sizeable primary surplus, albeit at a slower pace than currently. Our working assumption is that before that target is reached, the region will agree on a more aggressive restructuring of official loans."

(Additional reporting by Jan Strupczewski; Writing by Luke Baker; editing by Janet McBride)