After the first round of voting on Sunday, Hollande came out top with 28.6% of votes, whilst Sarkozy had only 27.1%.
Many people are now speculating that this could indicate an uphill struggle for a second term as president for Nicolas Sarkozy.
Mr Hollande said of the voting; "The choice is simple, either continue policies that have failed with a divisive incumbent candidate or raise France up again with a new, unifying president."
Mr Sarkozy - who has been in power since 2007 - said he understood "the anguish felt by the French" in a "fast-moving world".
One in five people voted for Marine Le Pen, who leads the far-right party National Front - the most popular the party has ever been - putting her in third place for the presidency.
After the vote, Ms Le Pen told jubilant supporters that the result was "only the start" and that the party was now "the only opposition" to the left.
The turnout on Sunday was extremely high at over 80%. The second round of voting will be in two weeks' time.