France's Hollande in strong parliament position

France's President Francois Hollande enters the voting booth in the legislative elections at the polling station in Tulle June 10, 2012.

PARIS (Reuters) - French President Francois Hollande is on track to win a solid parliamentary majority after a first-round election that leaves him strengthened heading into a flurry of talks with euro zone leaders that could make or break the currency union.

Sunday's vote left Hollande's Socialist Party bloc likely to win the 289 seats it needs for an outright majority in the 577-seat National Assembly, and almost certain to do so with its Greens Party allies on board, polling institutes said.

The seat projections indicated Hollande may not need to rely on eurosceptic hard leftists to pass legislation, relieving him of a potential headache as Berlin pressures its partners to start moving towards a fiscal union in Europe.

"The realization that the crisis is serious and that the government needs elbow room to get the country back on track is playing in favor of the government winning an absolute majority," said Stephane Rozes at the CAP political consultancy.

Socialists were muted in their reaction, anxious to keep the pressure on supporters to vote in next Sunday's runoff, but winning power in the lower house for the first time in a decade would be a triumph for the left after it took the Senate in 2011 and won the presidency in May after 17 years on the outside.

"Change is beginning," Prime Minister Jean-Marc Ayrault said, but warned: "Everything hinges on next Sunday."

Hollande needs a coherent majority to back him on upcoming adjustments to the 2012 budget to reflect sickly growth and on a broad tax reform he plans for the weeks ahead that will raise taxes on the wealthy to fund his spending plans.

Even more crucial will be possible legislation in the months ahead to grant European Union institutions more power over national budgets, something that would be hard to get lawmakers outside his party and the general public to swallow.

A lurch back into crisis has ramped up the pressure for the euro zone to mutualise its debt and create an integrated bank sector to protect depositors and governments, measures the bloc's paymaster Germany says it will only consider if member states agree to deeper fiscal integration.

Hollande broadly supports the integration that Merkel is now demanding, but being reliant on hard leftists or conservatives to grant more budget power to Brussels would run the risk of calls for a referendum and could trigger street protests.

Hollande flies to Rome on Thursday to discuss the crisis with Italian Prime Minister Mario Monti. The pair will rub shoulders with German Chancellor Angela Merkel and Spanish Prime Minister Mariano Rajoy at a G20 summit in Mexico on June 18-19 - right after the parliamentary second-round and a Greek election.

SCANT HONEYMOON

The euro zone crisis has provided fodder for National Front leader Marine Le Pen, who built on her strong score in the presidential race by taking a commanding lead on Sunday in a northern French working class town.

With anger over the economy the single biggest motivation for French voters today, Le Pen's party is at its closest in years to winning a parliamentary seat, having candidates in four constituencies qualified to go through to the second round.

Hollande, who won the presidency due largely to a rejection of conservative Nicolas Sarkozy and his failure to curb rampant unemployment, has been given a short honeymoon by voters. Fewer than two-thirds give him positive approval ratings in surveys.

The president is set to announce budget adjustments by the end of June after a national audit office assessment of public finances that is expected to show growth is flagging.

Those adjustments could include spending cutbacks or delays, given the pressure on France to cut its deficit. A parliamentary majority would be a boon for Hollande in that case.

Initial projections based on a partial count of Sunday's vote suggested Hollande's core Socialist bloc could win 283 to 329 seats in the 577-member National Assembly in the runoff.

With the Greens, the government would have 295 to 347 seats, the CSA polling institute forecast, well ahead of the mainstream conservatives with 210 to 263 seats. The Left Front of radicals and Communists could make an impact with a projected 13-19 seats but its firebrand leader Jean-Luc Melenchon did not win a seat.

None of Hollande's key ministers were seen at risk of losing their seats - which would mean them having to quit the cabinet.

Ayrault, along with Foreign Minister Laurent Fabius and European Affairs Minister Bernard Cazeneuve were all re-elected on Sunday by winning more than 50 percent straight off. Finance Minister Pierre Moscovici, who like Hollande is staunchly pro-European, was on track to win a three-way runoff on Sunday.

(Additional reporting by Emmanuel Jarry; Editing by Jon Hemming)