Pre-election polls suggest far-right nationalist Marine Le Pen and Emmanuel Macron, an independent centrist and former economy minister, were in the lead.
The 39-year-old French national who shot and killed a police officer in Paris just days before the nation's presidential vote was armed to the teeth, had a long criminal record and spent more than a decade in prison for other violent crimes, including trying to attack cops, officials say.
While Sunday's results looked broadly in line with polls, failures to predict the outcome of the Brexit referendum and US elections had shaken investors' trust in them.
Amid heightened security, French voters began casting ballots for their next president Sunday in a first-round poll that's being seen as a litmus test for the future of Europe and the spread of populism around the world.More news: Polls Open in France's Pivotal Presidential Election
But conservative Francois Fillon is making something of a comeback after being plagued for months by a fake jobs scandal, and leftist Jean-Luc Melenchon's ratings have surged in recent weeks.
The possibility of a Le Pen-Melenchon run-off is not the most likely scenario but is one which alarms bankers and investors. His lack of a national party organization did not matter much in the presidential election, but it could be fatal in the parliamentary elections.
While Le Pen faces the runoff as the underdog, it's already stunning that she brought her once-taboo party so close to the Elysee Palace.
Almost 47 million voters will decide whether to back a pro-EU centrist newcomer, a scandal-ridden veteran conservative who wants to slash public spending, a far-left eurosceptic admirer of Fidel Castro or to appoint France's first woman president who would shut borders and ditch the euro.More news: North Korea displays apparently new missiles as USA carrier group approaches
"You are the faces of French hope", he said. With the immediate threat of Le Pen out the way, the center-right and center-left parties may be more likely to return to their usual bickering, and in particular their resentment of the young upstart. Le Pen wants the country to leave the European Union and impose a moratorium on all immigration.
There are contradictory lessons to be taken from this first round vote. "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 which will be positive for risk appetite on Monday morning", said Rabobank's head of rates strategy in London, Richard McGuire. Proclaiming that "the left is not dead", he also urged supporters to back Macron.
Even if Le Pen springs a surprise on May 7, her "Frexit" ambitions will require constitutional change which experts say will be hard, especially as her National Front party only has a handful of federal lawmakers and is seen as highly unlikely to win anything like a majority in June's parliamentary elections.
Socialist presidential candidate Benoit Hamon, who was far behind in Sunday's results, quickly conceded defeat.More news: Pence visits carrier as questions emerge over trump's 'armada'
But previous militant attacks, such as the November 2015 killing of 130 people in Paris ahead of regional polls, did not appear to boost the votes of those espousing tougher national security policies.
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