Voting was underway in France on Sunday for the first round of presidential election amid tight security following a terror attack in Paris earlier this week.

A total of 66,500 polling stations across the country opened at 8 a.m. and will close at 8 p.m. Exit polls are expected soon thereafter.

French overseas territories began voting on Saturday. Forty-seven million registered voters are eligible to vote, the Guardian reported.

The top two finishers from the 11 candidates in the first round will advance to a runoff on May 7 to decide the next President after a tense and tight election dominated by the economy, jobs, immigration and national identity.

Four candidates are seen as being within reach of the presidency: the conservative Francois Fillon, the far-right leader Marine Le Pen, liberal centrist Emmanuel Macron and the far-left's Jean-Luc Melenchon.

President Francois Hollande is not seeking a second term and is the first French President in modern history to do so.

More than 50,000 police and 7,000 soldiers are on duty in France, which has been in a state of emergency for more than 18 months after a wave of Islamist attacks that have killed 239 people since January 2015, the Guardian reported.

On Thursday, Karim Cheurfi, who had served 14 years in prison for violent crimes including the attempted murder of two policemen, shot dead officer Xavier Jugele on the Champs-Elysees in Paris. Cheurfi was later killed by security forces.

The attack was claimed by the Islamic State (IS) terror group.

The main candidates cancelled campaign events on Friday -- the last day of campaigning -- and instead made televised statements in which they competed to talk tough on security and vowed a crackdown on IS, reports CNN.

Political analysts have said the race between the leading contenders is considered too close to call, the BBC said.

No candidate is expected to get the 50 per cent of votes required for an outright win.