* Polls show Hollande set for Socialist bloc majority
* Hollande preparing tax and other economic legislation
* National Front set to win seats for first time since 1980s
PARIS, June 17 (Reuters) - President Francois Hollande is on track to win a Socialist bloc majority in France's parliamentary election run-off on Sunday that would bolster his position in looming legislative battles over euro zone crisis policy.
A clear majority reliant neither on opposition conservatives nor eurosceptic hard leftists, as opinion polls point to, 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 the French public in no mood to suffer further economic gloom, Hollande will have no time to bask in glory.
Opinion polls and seat 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.
But just as his own May 6 election celebrations were kept short by Europe's ballooning crisis, Hollande flies to Mexico early on Monday, with voting slips barely counted, for the first of a flurry of summits that need to reach watertight accords.
A month into his presidency, Hollande's decision to identify with southern nations weary of austerity measures has sparked a rift with Europe's chequebook-holder Germany that the Socialist needs to fix fast.
Further down the line, Hollande faces challenges keeping eurosceptic Socialist lawmakers fully behind him if he agrees to Germany's demand for a swift commitment to deeper fiscal and politician integration in Europe.
He may also encounter resistance within his party to any decision to slow down spending plans after a public finance audit due at the end of June that is expected to show France poorly placed to meet its deficit-cutting goals.
"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 open at 8 a.m. (0600 GMT) and the last ones close 12 hours later, with some concern over turnout as the nation is asked to vote 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 would throw its future in the euro zone into question 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. Of the remaining 541 constituencies, most run-offs are between two candidates, although 34 constituencies will see three-way contests between rivals who all won the qualifying 12.5 percent.
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 firebrand 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, giving him scores in the low 60s in popularity surveys, suggests they will react angrily if he announces spending cutbacks or big rises in social contributions to meet deficit targets.
Some analysts see street protests ahead. "My hypothesis is that after the (summer) holidays there will be social upheaval as people will no longer be able to express their frustration through voting," said political scientist Dominique Reynie.