June 11 (Reuters) - Sterling hit a 22-month high versus the euro after a sharp rise the day before and was roughly unchanged against the dollar on Wednesday as investors await U.S. inflation data and the outcome of the Federal Reserve policy meeting on Wednesday.

The single currency dropped on Monday after the gains of eurosceptics in the elections for the European Parliament and France called an election.

With a potential right-wing victory in France, the political landscape could pose significant challenges to the European Union's efforts to deepen integration, weakening the euro.

Britain's labour market showed more signs of cooling in April with a rise in the unemployment rate but failed to trigger a significant price action of the British currency.

The dollar hovered near a one-month peak against the euro as traders braced for U.S. data and the Fed rates forecasts.

Sterling rose 0.25% to 84.33 pence per euro, its highest since August 2022.

It was up 0.05% at $1.2738.

Derek Halpenny, head of research, global markets at MUFG, flagged that the euro has broken below important technical support at the 0.8500 level, which has been tested and held over the past year.

He expects the single currency to rise back up into the 0.8500-0.8600 trading range if Marine Le Pen's National Rally (RN) fails to become the largest party in France and to fall towards the lows in early 2022 at closer to the 0.8300 if the RN party becomes the largest party but falling short of being able to form a majority in parliament.

The NR was forecast on Monday to win a snap election in France but fell short of an absolute majority.

"Sterling largely held its own off the back of the data, as while rapidly rising wages could delay the start to Bank of England interest rate cuts, the increase in joblessness bodes ill for the UK's growth outlook," said Matthew Ryan, head of market strategy at global financial services firm Ebury.

Money markets discounted a 40% chance of a 25 basis points BoE rate cut in August while more than fully pricing the same move in November.

(Reporting by Stefano Rebaudo; editing by Angus MacSwan)