Hollande announced yesterday he would not seek re-election next April, bowing to historic low approval ratings.
"I have decided that I will not be a candidate," the 62-year old Hollande said in a solemn televised address from the Elysee Palace in Paris.
Manuel Valls, who had been a loyal prime minister to Hollande until recently but hinted at the weekend he might run against his boss in planned primaries, is expected to throw his hat in the ring.
"In the months to come, my only duty will be to continue to lead my country," he said.
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The Socialist leader has some of the lowest approval ratings for a French president since World War II.
His term has been marked by U-turns on major policies, terror attacks, a sickly economy and embarrassing revelations about his private life.
A new poll on Wednesday predicted he would win just seven percent of votes in the first round of next year's election -- strengthening Socialist Party critics who view him as a lame duck.
But the full range of candidates remains unknown and the role of independents such as 38-year-old ex-economy minister Emmanuel Macron are difficult to predict.
The emergence of Fillon threw up a surprise in itself. At the start of the rightwing primary, he was considered a distant third, only to roar through the field and win comfortably.
Hollande's decision flings open the door to others vying to be the Socialists' champion.
The party began accepting candidates on Thursday for its primaries, due on January 22 and 29. The presidential elections are due on April 23, with a runoff on May 7.