Voters are deciding between 12 candidates, including incumbent Emmanuel Macron, far-right candidates Marine Le Pen and Eric Zemmour and far-left Jean-Luc Mélenchon.
While Mr Macron has long appeared to be the favourite to win, Ms Le Pen has seen a surge in the polls in recent days.
Polls now put Macron still in the lead with about 26 percent, with Le Pen following close behind at 25 percent.
Luc Rouban, a political scientist at Sciences Po in Paris, said: “Marine Le Pen has never been this close to clinching the presidency.”
The two candidates who gain the most votes in the first round will move on to the second round, which will take place on April 24.
Official results will be published later tonight, with first projections from polling institutes going live from 8pm.
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