* Attention back on monetary policy outlook for Europe, U.S.
* Yen, Swiss franc weaken
* U.S. yields rise on Fed rate hike expectations (Updates prices, adds comment)
By Gertrude Chavez-Dreyfuss
NEW YORK, May 9 (Reuters) - The dollar climbed to nearly two-month highs against the yen on Tuesday as risk appetite improved following the French election and investors focused on monetary policy and likely upcoming Federal Reserve interest rate hikes.
U.S. benchmark 10-year Treasury yields hit five-week highs, with rate futures pricing in close to a 90 percent chance of an interest rate increase next month. Yields on U.S. two-year notes, the tenor most sensitive to rate hike expectations, also advanced on Tuesday, climbing to eight-week peaks.
The dollar index, tracking the greenback's value against six major currencies, rose to a three-week high, in line with the gains in yields.
James Chen, head of research at Forex.com in Bedminster,New Jersey, said the dollar should remain supported in the near term because of a generally stable U.S. economy and a Fed that is on a distinct tightening path.
He noted that dollar/yen should continue to rise as a result, "especially if market risk perceptions and volatility remain subdued."
Chen sees further momentum on the currency pair, with the next major upside targets at 116.00 and 118.00 yen.
The interest rate premium investors receive for holding dollar 10-year government bonds instead of their yen equivalents rose to its highest since the end of March overnight.
In late trading, the dollar was up 0.9 percent against the yen at 114.28 yen , after earlier hitting its highest level since mid-March. The euro also rose against the yen, up 0.4 percent at 124.20 yen.
The Swiss franc, another currency with firmly negative interest rates as well as a central bank seeking to weaken it with market intervention, fell to its lowest against the euro since mid-October.
The euro was last up 0.5 percent at 1.0966 francs, while the dollar rose 1.0 percent to 1.0051 francs.
Market measures of volatility for euro-dollar rates have hit their lowest in three years in the past week and Deutsche Bank strategist Oliver Harvey warned in a note on Tuesday of the risks of a turn in that trend.
"One of the main themes this year has been the fall in vol ... but there are increasing signs a turning point is close," he said, pointing to the risks of downbeat signals on global growth and the chances of the Fed outpacing expectations on future policy moves.
The euro dipped back below $1.09, down 0.5 percent, falling from six-month highs hit after centrist Emmanuel Macron's victory in the French presidential election on Sunday.
Reporting by Gertrude Chavez-Dreyfuss; Additional reporting by Patrick Graham in London; Editing by Meredith Mazzilli and Peter Cooney