NEW YORK/LONDON, June 10 (Reuters) -

The euro fell on Monday after gains by the far right in European Parliament elections on Sunday prompted French President Emmanuel Macron to call a snap national election.

The uncertainty in France adds one more element to what will be a busy week for markets with U.S. inflation data due on Wednesday, the same day as the Federal Reserve's policy decision at its two-day meeting, and a Bank of Japan meeting on Friday rounding off the week.

The euro was last down 0.4% against the dollar at $1.076 and got as low as $1.0733, its lowest since May 9. It also fell 0.4% on sterling to a near two-year low of 84.52 pence , and was last down 0.4% on the Swiss franc at a seven-week low of 0.9648 francs.

The increase in support for right wing parties was "generally what was expected, but the surprise element is that Macron has reacted by calling a snap election, so that makes the market more nervous," said Lee Hardman, senior currency analyst at MUFG.

The U.S. dollar was also boosted after Friday’s jobs report showed that employers added more jobs than expected in May, while wages also rose more than anticipated, leading traders to pare back expectations that the U.S. central bank will cut rates as soon as September.

"The market was clearly caught wrong footed," said Paula Comings, head of foreign exchange sales at U.S. Bank in New York.

Wednesday’s consumer price index (CPI) for May will be the next major data point to drive Fed expectations.

If inflation comes in softer, “the market's going to feel some relief. I think the dollar could weaken, but probably not out of its recent range,” said Comings.

If it is high, however, "euro/dollar would continue to trade down towards the lower end of the range" and it will "impact (emerging market) currencies disproportionately," Comings said.

Fed officials have said that they want to see several months of inflation falling back closer to their 2% annual target before cutting rates.

Economists polled by Reuters expect headline consumer price inflation to ease to 0.1%, from 0.3% last month, and core price pressures to remain steady on the month at 0.3%.

A New York Fed survey on Monday showed that the U.S. public’s outlook on the future path of inflation was mixed in May, though inflation is seen as being 3.2% a year from now, compared with April’s expectation of 3.3%.

Fed policymakers will update their economic and interest rate projections when they conclude their two-day meeting on Wednesday.

At the last such release in March, the median projection was for three 25 basis point cuts this year and investors anticipate the new forecast will show an expectation of fewer rate reductions.

The dollar index was last up 0.09% at 105.15 and earlier reached 105.39, the highest since May 14.

The paring back of expectations for rate cuts has been supporting the dollar for much of 2024, with the Japanese yen in particular suffering due to the large interest rate gap between the U.S. and Japan.

The dollar was last up 0.25% on the Japanese currency at 157.08 yen, the highest in a week..

The Bank of Japan will hold its two-day monetary policy meeting on Thursday and Friday, with the central bank widely expected to maintain short-term interest rates in a 0-0.1% range.

Reuters reported last week that BOJ policymakers are brainstorming ways to slow its bond buying and may offer fresh guidance.

In cryptocurrencies, bitcoin gained 0.71% to $69,768.

(Reporting by Karen Brettell and Alun John; Editing by Mark Potter, William Maclean and Chizu Nomiyama)