Francois Hollande's victory is likely to have a big impact on the eurozone, with the president-elect pledging to renegotiate the EU treaty on government debt.
In Greece, the ruling coalition was dealt a huge blow in parliamentary elections by voters who reject austerity measures - leaving the country's multi-billion pound eurozone bailout at risk.
Among European markets early on Monday, Germany's DAX (Xetra: ^GDAXI - news) dropped 1.5% and France's CAC (Frankfurt: 924169 - news) -40 shed 1.6%. However, by the afternoon, most European markets had recovered.
Greek shares suffered a lot more - trading 8.2% lower at one point. The Greek market closed down 6%.
In the Far East, there was heightened uncertainty amid concerns about Europe's ability to solve its debt crisis.
Financial consultant Iain Anderson, from Cicero Group, told Sky News it had been "a sea of red" in Asian markets.
"They may be celebrating at the Bastille but they're not really looking forward to Europe's woes in Asia," he said.
"I think we're going to have a very turbulent ride over the next few days and weeks."
He added: "It's absolutely vital that Greece can form a government over the next three days.
"If it cannot, I think there will be real concerns and equally, everyone watching in Asia that first meeting between Hollande and Angela Merkel - we'll see how that goes."