Security around the more than 60,000 polling stations was tightened up in wake of the deadly shooting on the Champs-Elysses on Thursday, which left one police officer and a gunman dead.
The government mobilized more than 50,000 police and gendarmes to protect the polling places and an additional 7,000 soldiers were on patrol.
It is the first time in recent memory that a presidential election, in which 47 million people are eligible to vote, taking place during a state of emergency, which was put in place after the Paris attacks of November 2015.
But conservative Francois Fillon, a former prime minister, appeared to be closing the gap, as was far-left candidate Jean-Luc Melenchon.
Political campaigning was banned from midnight Friday hours ahead of polls opening in France's far-flung overseas territories such as Guadeloupe, French Polynesia and French Guiana, which all voted a day early Saturday.