The euro jumped to a five-month high after the first round of voting in the French presidential election on Sunday.
Centrist Emmanuel Macron topped the voting, going through to the final round with far-right Marine Le Pen.
Investors worried that far-left Jean-Luc Mélenchon would beat Mr Macron, giving voters a choice between two Eurosceptic candidates.
The euro initially rose 2% to its highest level since mid-November before giving up some ground.
Asian markets were trading higher on Monday, with Japan’s Nikkei 225 at one point surging about 1.5% before retreating slightly.
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Octavio Marenzi, chief executive of the financial research consultancy Opimas in Paris, said: “Macron will be reassuring to markets, with his pledge to lower corporate taxes and to lighten the administrative burden on firms. He basically represents continuity.”
That view was shared by Kathleen Brooks, research director at City Index, in London, who said the result was positive for two reasons.
“Firstly, Macron is a politically stable, centrist candidate, almost like France’s Obama… He is considered a safe pair of hands. Secondly, it helps to solidify the future of the EU and the euro, something that Marine Le Pen wants to destroy.”
In addition to a further strengthening of the euro, she expects the main share markets in Germany and France – the Dax and Cac 40 – to rise on Monday.
As early results started coming in, the euro jumped 2% against the dollar to $1.09395, its highest level since 10 November, the day after the results of the US presidential election. It later fell back slightly to $1.0855.
Against the yen, which investors tend to flock to when they perceive high levels of risk, the euro jumped as much as 3% to trade at a five-week high before edging down a bit to 119.50 yen.
Against sterling, the euro was 1.2% higher at 0.8480 pence.
The euro’s rally underlined investors’ nervousness, analysts said. “The market’s initial reaction was stronger than expected. It means that many people had their guard up ahead of the vote,” said Yuji Saito, Tokyo-based forex director at Credit Agricole.
Rallying around Macron
Mr Macron, a former investment banker, served as economy minister under current President Francois Hollande. Despite his relative inexperience – he has never served as an MP – polls see him defeating Ms Le Pen in the second round.
Richard McGuire, head of rates at Rabobank, said: “The assumption now is that centrist voters will rally around Macron, denying Le Pen the presidency and hence this will effectively be a pro-establishment, pro-European result.”
Mr Macron’s defeated rival in Sunday’s election, François Fillon, has already endorsed him. Other senior political figures in France, including former Prime Minister Alain Juppe, have also thrown their weight behind Mr Macron.
However, Mr McGuire cautioned that, after the UK Brexit vote and the election of Donald Trump in the US, no one should take anything for granted ahead of the second round on 7 May.
Pro-European Mr Macron was the Socialist finance minister until the autumn, when he quit to set up the En Marche movement, which proposes tax and spending cuts.
The anti-EU Ms Le Pen’s campaign focused on jobs, security and the threat from Islamic extremism.
Bookmakers made Mr Macron the firm favourite to win the run-off, with both Ladbrokes and Coral offering 1-6 and William Hill 1-8, with Ms Le Pen at 4-1, 7-2 and 9-2 respectively.
Read more at BBC.co.uk