A man casts his ballot during the second round of voting in the French presidential elections on Sunday. AFP

Voting was underway on Sunday in the French presidential run-off in which people will make a choice between incumbent President Emmanuel Macron and his far-right challenger Marine Le Pen as their new leader.

French voters began casting their ballots on Sunday, after a fractious campaign that has seen the far right come its closest yet to winning power.

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Voting began at 8am and is scheduled to end at 8pm, reports Xinhua news agency.

Eligible voters on French overseas territories have already cast their ballots on Saturday.

Pictures of Emmanuel Macron (left) and Marine Le Pen are displayed in the French presidential elections. AFP

According to the results of the first round voting on April 10 published by France's Constitutional Council, Macron won 9,783,058 votes, or 27.85 per cent of valid ballots, while Le Pen garnered 8,133,828 ballots, or 23.15 per cent.

Macron went into the election with a stable lead in opinion polls, an advantage he consolidated in the frenetic final days of campaigning, including a no-holds-barred performance in the pre-election debate.

But analysts have cautioned that Macron, who rose to power in 2017 aged 39 as the country's youngest-ever modern leader, can take nothing for granted given forecasts of low turnout that could sway the result in either direction.

He must above all hope that left-wing voters who backed other candidates in the first round on April 10 will back the former investment banker and his pro-business, reformist agenda to stop Le Pen and her populist programme.

Voters queue to cast their ballots for the second round of France’s Presidential Election in Noumea. AFP

Some 48.7 million French are eligible to vote.

To take account of the time difference with mainland France, polls opened earlier in overseas territories, home to almost three million French.

The first vote in the election was cast midday on Saturday, Paris time, by a 90-year-old man in the tiny island territory of Saint Pierre and Miquelon, off the northern coast of Canada.

Polls subsequently opened in France's islands in the Caribbean and the South American territory of French Guiana, followed by territories in the Pacific and then the Indian Ocean.