Analysts said France's consistent downturn is "worrying" and serves to highlight just how fragile the recovery is.
"The sharp contrast between the latest French and German PMI prints throws the worrying divergences in the very core of the euro zone into sharp relief," said managing director of Spiro Sovereign Strategy, Nick Spiro.
(Read more: Euro zone business activity rises beyond expectations)
"While the recent data coming out of France has been something of a mixed bag, the weakness of French private sector output has become one of the most - if not the most - conspicuous features of the fragility of the so-called "recovery" in the euro zone," he added.
Chris Williamson, chief economist at Markit said the malaise in the French domestic economy is offsetting a better export performance, suggesting there is a risk of the French economy contracting again in the first quarter.
While France struggles to eke out any growth, optimism in the German economy remains strong. The recovery in the euro zone's largest economy is looking more and more sustainable, but the figures should give the ECB "some food for thought" according to economist Carsten Brzeski.
(Read more: The 'Merkel put' is a safe bet)
"The mild winter weather, low inventories and gradually filled order books bode well for economic activity in the coming months," said the ING senior economist.
The data, however, provides new ammunition for those accusing Germany of "beggar-thy-neighbour policies," said Brzeski as the German statistical office reported that real wages dropped by 0.2 percent year-on-year in 2013.
"This was the first drop in real wages since 2009. Over the last six years, German real wages have on average increased by an annual 0.5 percent. Too little to create a consumption boom but also too much to facilitate euro zone rebalancing," he said.
"Germany should offer lots of food for thought for the ECB. The German economy is powering ahead but at the same time it doesn't make euro zone rebalancing any easier. Combined with new deflation fears, this gives a cocktail with a high risk for a headache," he added.
—By CNBC's Jenny Cosgrave: Follow her on Twitter