* PM Valls says tax burden on French must be reduced
* Left wings say Hollande broke promises in Europe
* FN victory also a slap for opposition conservatives (Adds Hollande calls with other EU leaders)
By Mark John and Ingrid Melander
PARIS, May 26 French President Francois Hollande pledged on Monday to press ahead with reforms at home whilst pushing for the EU to change tack, saying the triumph of the French far right in European elections showed voters felt Europe was not protecting them.
In a televised address to the nation a day after the anti-immigrant, anti-EU National Front party won its first-ever nationwide poll, Hollande said this had been "a vote of mistrust towards Europe."
In response, he will tell EU leaders at a meeting on Tuesday evening in Brussels that they must now focus the 28-nation group on growth, jobs and investment, not on austerity.
"Europe has become illegible, distant, basically incomprehensible, even for governments. This cannot go on," Hollande said in a short message broadcast on television a day after his Socialist's party resounding electoral defeat.
Hollande said the government would not waver on its plans despite the defeat and would press ahead with economic, social and territorial reforms.
"I am a European, it is my duty to reform France and re-focus Europe," he said, adding that Europe should "withdraw itself from areas where it is not needed.".
Prime Minister Manuel Valls earlier on Monday promised more tax cuts but said France would still make the budget savings needed to bring its public deficit within EU limits. But, in a sign of potential clashes ahead, left-wingers in the ruling Socialist party said the election results vindicated their opposition to such cuts.
Hollande had phone conversations on Monday with fellow EU leaders including German Chancellor Angela Merkel, Spanish Prime Minister Mariano Rajoy and Italy's Matteo Renzi, his office said, as the EU faces a giant policy dilemma on which course to take.
FRANCE WEAKENED IN EUROPE?
France's deficit stood at 4.2 percent of output last year. Its EU partners have given it an extended deadline of 2015 to bring it within three percent.
However, Sunday's poll results will encourage the left wing of the Socialist Party to resist further tightening in future budgets.
"For years now, the Socialist Party has been unable to heal the rift between its leadership, its voters and the left-wing grass roots across Europe," the "Maintenant la Gauche" ("Now for the Left") group of left-wing Socialist deputies said.
"Francois Hollande's failure to keep his promise on changing the direction of Europe has only added to the disenchantment of our citizens, who are opposed to austerity and free markets."
Hollande's Socialist Party scored 13.98 percent of the votes on Sunday, its worst-ever performance in an EU election. The centre-right UMP stood at 20.80 percent, further behind the FN than predicted by pre-vote opinion polls.
Although the heavy abstention rate meant that barely one in 10 voters actually backed the FN, analysts said the vote showed how the country's political mainstream had failed to persuade voters that European integration still made sense for France.
"The legitimacy of France in Europe is weakened," Dominique Moisi of the French Institute for International Relations (IFRI) told Reuters TV.
"To function, Europe needs a strong balance between France and Germany. But France is moving the way of Italy or Greece in economic terms and moving the way of Britain in its relationship with Europe."
Valls, who on Sunday night called the FN win a political "earthquake" for founding EU member France, said it showed the government had to push ahead with plans to lower taxes, after many French were faced this year with sharply higher claims.
But aides to the prime minister said he was underlining his intention to push ahead with that overall reduction in the burden rather than announcing plans to go further and which would require financing with additional savings.
France has the highest tax take among developed countries after Denmark. The government has already said it aims to trim the tax burden from 45.9 percent of national income this year to 45.3 percent by the end of Hollande's term in 2017.
Just ahead of the EU election, the government had announced that 1.8 million households would be exempted from income tax later this year, at a cost to the state of 1 billion euros.
Asked if his government would maintain its goal of shaving 50 billion euros from public spending over the next three years as part of efforts to bring its public deficit to within EU limits, Valls replied that it would be "absurd" not to. (Additional reporting by Pauline Ades-Mevel, Elizabeth Pineau and Leigh Thomas; Editing by Mike Peacock, Larry King)