Initial projections after voting closed on Sunday placed centrist Le Marche! leader Mr Macron as the victor, with right-wing, anti-immigrant Front National leader Marine Le Pen just behind him.
If the first-round result is confirmed, it would put the 39-year-old pro-Europe Macron within striking distance of the presidency. She portrayed her duel with Macron as a battle between "patriots" and "wild deregulation" - warning of job losses overseas, mass migration straining resources at home and "the free circulation of terrorists".
Macron may face a hard task in winning sufficient backers in the French parliamentary elections in June, necessitating some kind of delicate political compromise with established centrist and left-wing parties.
Her supporters burst into a rendition of the French national anthem, chanted "We will win!" and waved French flags and blue flags with "Marine President" inscribed on them. Officers fired tear gas to disperse the rowdy crowd.
From Paris to Berlin, and Washington to Singapore, French voters lined up at polling stations yesterday to cast ballots, with the early turnout in France slightly down from the last election in 2012, amid fears that broad disillusionment with politics could keep voters away.More news: Saudi Arabia restores civil service and military allowances
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"The main thing at stake in this election is the rampant globalization that is endangering our civilization", she added while calling herself "the candidate for the people". If she were successful, it would probably sink an institution that has helped bind Europe together for decades.
After many years of high unemployment and a steady drumbeat of political scandals, voters turned their backs on the establishment and instead backed a political newcomer in Macron and a far-right candidate in Le Pen.
Voting took place amid heightened security in the first election under France's state of emergency, which has been in place since gun-and-bomb attacks in Paris in 2015.
Several hundred young people rallied in the Bastille square - the historic site where the 1789 French Revolution began - after projections suggested Le Pen would contest the second round against Emmanuel Macron, a centrist and former banker.
Socialist presidential candidate Benoit Hamon, who was far behind in Sunday's results, quickly conceded defeat.