Hollande is to announce a new government on Tuesday. The debate among French Socialists mirrors one taking place across Europe on whether to pursue a German-led model of fiscal austerity or use more government spending to spur growth.
Prime Minister Manuel Valls offered up his Socialist government's resignation after accusing France's outspoken economy minister of crossing a line with his blunt criticism of the government's policies. Hollande accepted the resignation and ordered Valls to form a new government by Tuesday.
Hollande has promised cuts to taxes and spending as well as reforms to make it easier for businesses to open and operate. The measures are meant to reduce the tax burden for companies and also contain the government's deficit, which is above the European Union's limit of 3 percent of GDP.
France has had effectively no economic growth this year, unemployment is hovering around 10 percent and Hollande's approval ratings are sunk in the teens. The country is under pressure from the 28-nation EU to get its finances in order, but Economy Minister Arnaud Montebourg has criticized austerity as the wrong medicine to foster growth and argues the government should spend more freely to create jobs.
He lashed out at the government's policies in a final adieu as minister on Monday.
"The entire world is urging us --even begging us -- to end these absurd austerity policies that are plunging the eurozone into an economic slowdown," he said in a statement to the press.
"My responsibility as economy minister is to tell the truth, and observe... that not only these austerity policies are not working, but they are also unfair, as well as being ineffective"
Hollande's promised reforms have stalled, in large part because of the divisions within his Socialist Party.
Montebourg unsettled his government bosses over the weekend by proclaiming that a "major change in our economic policy," was needed -- just days after Hollande had expressly said there would be no change in the government's economic direction.
The minister's comments angered the Socialist leadership, which said Montebourg's job was to support the government, not criticize it from within.
"He's not there to start a debate but to put France back on the path of growth," Carlos Da Silva, the Socialist Party spokesman, told the Le Figaro newspaper.
Montebourg represents the hard-left Socialist base, and his departure from the government is likely to anger many of the voters who brought Hollande to office in 2012. Since that time, France's economy has only worsened, and the sense of impending crisis weighs heavily.
Montebourg was conducting a "very responsible and constructive debate on questions that we have been asking for months," said Christian Paul, a Socialist parliamentarian who is among a clutch of leftist rebels backing Montebourg. "It looks like a schoolyard punishment."
French officials have already made clear the deficit will again surpass the EU's 3 percent limit and are negotiating a delay.
The new government is unlikely to include Montebourg or other left-wing Socialists and there will be no new election. Instead, led by Valls, the new Cabinet is expected to work toward smoother ties with the EU.
Montebourg's criticism of austerity -- and his pointed remarks about German Chancellor Angela Merkel -- have rankled before.
In an interview last week with the newspaper Le Monde after Germany's economy also showed signs of stagnation, Montebourg said France's neighbor had been "trapped by the policy of austerity."
He went on to say "when I say Germany, I mean the German right wing that supports Angela Merkel. It's not France's job to align itself to the ideological axioms of Germany's right wing."
Merkel on Monday declined to comment directly about France's change in government but said she wishes "the French president success with his reform agenda."
The Socialists still have a majority in parliament, but one that will remain fractured even after the new government is installed -- and vulnerable to inroads from France's resurgent right-wing National Front.
"It looks more like an atmosphere of purge than an atmosphere of reconstruction," said Paul. "The president is diminishing his majority at every step."