France's recession is likely to pile more pressure on the country's finance ministry, at a time when infighting has already led one senior politician to fuel rumors that Finance Minister Pierre Moscovici could be replaced.
The euro zone's second largest economy is suffering from record unemployment and waning business and consumer confidence. Official data on Wednesday showed that its economy had contracted by 0.4 percent year-on-year and 0.2 percent quarter-on-quarter in the first quarter, officially entering a recession.
A string of clashes between Moscovici and left-wing Industry Minister Arnaud Montebourg has led former prime minister Laurent Fabius to call for better leadership at the finance ministry, which is also known as "Bercy".
(Read More: France's Moscovici Says 'Non' to Austerity)
"I ran Bercy in the past and it's true that it needs a boss," current Foreign Minister Fabius told French radio station RTL on Tuesday.
"At the moment you have several bosses. Whatever the quality of the men and women and their level of agreement, I think that stronger coordination would be more useful."
The comments came after President Francois Hollande, celebrating his one-year anniversary in power amid dwindling approval ratings, told French magazine Paris Match that none of his ministers were indispensable and all would be judged on their results.
On Thursday, President Hollande said a cabinet reshuffle was possible, but he wasn't going to do one right now.
An economist at a France bank who preferred to remain anonymous said there was a "50-50 chance" that Francois Hollande would change his lineup in the next few weeks.
"I think Francois Hollande does not dislike the idea anymore, but does not know what to do. Each option carries a big risks, that would be very much the man: he hesitates for a long time and then suddenly decides, acts and sticks to the decision," he told CNBC.
Michel Martinez, an economist at Societe Generale said on Thursday that the number of cabinet members is likely to be reduced. There are 37 ministers at present.
(Read More: France Slides Into Recession, Germany Disappoints)
"Prime Minister Ayrault would remain in charge. We see this reshuffle likely with this new government sticking to its pro-reform and deficit reducing agenda."
Meanwhile, Moscovici – who has been given two extra years to reduce France's budget deficit to within European Union (EU) limits - said he would use the time to push on with structural reforms.
Amit Kara, a European economist at UBS, told CNBC that France has some "difficult decisions" to make. "The government made a good start on labor market reforms, but the progress on product market reform has been all but non-existent," he said told CNBC.
With ministers openly discussing a reshuffle and socialist politicians voting against their government, talk has turned to who might replace Moscovici if he were moved.
(Read More: Eurogroup Chief: France Must Speed Up Reforms)
Media reports have also named Pascal Lamy, the outgoing director general of the World Trade Organization, and Louis Gallois, former CEO of defense firm EADS, as candidates for the role.
"[Gallois] would be criticized as he has no political experience," the source said, but added that he would be well received by the markets.
Kara, meanwhile, said he believed that a jump in bond yields - which are currently at around 2 percent on the benchmark 10-year sovereign - would do more to focus the minds of stakeholders than almost any individual policy maker.
"Will a new finance minister help? Possibly, but for France (or for that matter any European economy) to make major structural changes, we need the discipline of financial markets," he said.
—By CNBC.com's Matt Clinch; Follow him on Twitter