By Kevin Buckland

TOKYO (Reuters) - The U.S. dollar hung near a multi-week low versus major peers on Tuesday, still smarting from Friday's unexpectedly soft jobs report as traders awaited testimony from Federal Reserve Chair Jerome Powell for clues on the path of interest rates.

The euro held its ground after Monday's sharp swings as investors come to terms with a hung parliament in France, which points to potential political gridlock but removes many fiscal concerns stemming from far-right or leftist victories.

The U.S. dollar index, which measures the currency against the euro, sterling, yen and three other major peers, was flat at 104.99 in early Asian hours, sticking close to the overnight low of 104.80, a 3 1/2-week trough.

The index slumped 0.9% last week, exacerbated by Friday's monthly payrolls report, which boosted bets for the Fed to soon start cutting rates.

Traders currently set about 76% odds for a rate cut at the September meeting, up from 66% a week ago, according to the CME Group's (NASDAQ:CME) FedWatch Tool. Another cut is expected by December.

Chair Powell gives two days of testimony before Congress, beginning later on Tuesday with the Senate and followed by the House on Wednesday.

Consumer price data on Thursday could also be crucial, market watchers said, with recent numbers showing a cooling from unexpectedly high levels at the start of the year.

"All ears will be on how Powell communicates the risks between stubborn inflation and unnecessary labour market deterioration," said Ray Attrill, head of FX strategy at National Australia Bank (OTC:NABZY), who expects the U.S. dollar to decline over the longer term.

Meanwhile, markets have taken "a fairly sanguine view" of the French poll results, Attrill added, "viewing political gridlock - and with that a high degree of fiscal policy inertia - as the most likely way forward for France, a more benign scenario than any of the alternatives."

The euro was little changed at $1.0827, sitting not far from Monday's nearly four-week peak of $1.0845. The single currency also dipped as low as $1.07915 that same day.

Sterling traded flat at $1.28085, after rising as high as $1.28455 on Monday, its strongest since June 12.

The yen was steady at 160.91 per dollar, finding some equilibrium this week after rebounding from Wednesday's nearly 38-year trough of 161.96.