* Greek election raises doubts about bailout scheme
* Euro hits 3-mth low vs dollar, 3-1/2 yr low vs pound
* Euro/dollar has support at $1.2950
* Hollande victory seen raising uncertainty on Paris-Berlin unity
* Aussie falls, yen gains on broad risk averse sentiment
TOKYO, May 7 (Reuters) - The euro tanked on Monday, breaking below its well-worn range from the past three months against the dollar after elections in Greece and France raised fresh concerns that the euro zone's hard-earned bailout and austerity steps could fall apart.
In particular, the apparent failure of two pro-bailout ruling parties in Greece to win a majority in the parliament is throwing the future of the bailout scheme for the country into doubt.
With 95 percent of votes counted, the conservative New Democracy (ND) and socialist PASOK, which have dominated Greece for decades, are seen falling short of the 151-seat threshold needed for even the most fragile majority in parliament.
"The PASOK did unexpectedly poorly in the election ... Until we have more clarity on how the coalition government will be formed and what the new government will do with the bailout scheme, the euro will stay under pressure," said Masafumi Yamamoto, chief FX strategist at Barclays.
The euro fell as far as $1.29552, its lowest since Jan. 25, breaking below the rough $1.30-$1.35 trading band it had been stuck in since February. The euro last traded at $1.2978, down 0.8 percent from late U.S. levels last Friday.
For now, the euro has support at $1.2950, a major option barrier and the 61.3 percent retracement of its rally from its January low to a high in February, although uncertainty on Greece could overwhelm this.
"Things look really fragile. We'll have to see whether the ND can form a government," said a trader at a Japanese bank.
Another source of uncertainty, albeit a small one compared to developments in Athens, comes from France, where Socialist Francois Hollande swept to victory, ousting centre-right incumbent Nicolas Sarkozy.
While that outcome had been widely expected, some market players worry that Hollande's focus on growth measures to temper austerity could put Paris on course to clash with Germany's insistence on tough deficit reductions.
German Chancellor Angela Merkel's conservatives were in danger of being ousted from power in the German state of Schleswig-Holstein after her party suffered its worst showing since 1950 in a local election on Sunday, boding ill for another local election next Sunday in North Rhine-Westphalia, Germany's most populous state.
"Will Hollande and Merkel be able to push through needed eurozone wide agreements in the way Merkel and Sarkozy were?," asked Jens Norvig, strategist at Nomura, in notes to clients.
The euro also fell to 103.24 yen, its lowest level since mid-February and to 80.37 pence, a trough last seen in November 2008.
Disappointing jobs data from the U.S. on Friday added to the euro zone jitters, leading traders to cut exposure to risky assets, including the Australian dollar.
The Aussie fell to as low as $1.0110, its low so far this year, though upbeat Australian retail sales data helped it recover slightly from lows. It last stood at $1.0130, down 0.5 percent.
The yen, traditionally a safe-haven currency due in part to Japan's net foreign assets, gained against the dollar, which slipped 0.15 percent to 79.78 yen.
The U.S. dollar fell back below the 80 yen mark, seen as a support, on Friday after data showed US employers added 115,000 workers to payrolls last month, a third straight month of slowdown in hiring.
Still, the dollar was supported above two-month low of 79.64 yen hit last week, with another support seen at 79.14 yen, a 61.8 percent retracement of its rally from February to March.
Many market players say these support levels are likely to hold for the time being.
"The momentum of U.S. growth is slowing. Still, the economy looks in much better shape than last year," said Minori Uchida, senior currency analyst at the Bank of Tokyo-Mitsubishi UFJ
"Foreign players are also wary of the risk of more credit downgrades on Japan... There are no strong reasons to be long in the yen," he added.
A senior official of Standard & Poor's said last week that Japan is in danger of slipping from its AA- credit rating if reforms are held up as its unpopular government struggles to get support for tax measures.
Japan's trade surplus -- a source of the yen's strength for decades -- is vanishing as the country imports more fossil fuels after the Fukushima disaster last year.
The country shut its last active nuclear reactor on Saturday, leaving it with no nuclear-derived electricity for the first time since 1970.