Economically, the worry is that insistence on fiscal austerity by an out-performing Germany will delay an upturn in France, which has been steadily losing competitiveness to its larger neighbour.
Politically, the risk is that already uneasy relations between French President Francois Hollande and German Chancellor Angela Merkel could come under further strain when the euro zone needs strong, cohesive leadership to create a new institutional framework for the euro.
Philippe Waechter, chief economist at Natixis Asset Management in Paris, said signs of a solid recovery in Germany's economy were bolstering Merkel's position on economic policy going into September's general election.
Hollande, by contrast, was forced to acknowledge on Tuesday that growth would fall short of his government's 0.8 percent forecast. His government has already admitted it will miss its deficit target this year.
"The issue is how the balance of power evolves between Francois Hollande and Angela Merkel, knowing that France and Germany are extremely important in the political construction of the euro zone," Waechter said.
IMBALANCE OF POWER
Paris is more in tune with Italy and Spain than with Germany in wanting to put growth before deficit reduction and structural reform.
But the difficulty for Hollande as he seeks political support to counterbalance Berlin is that Italy holds a February 24/25 election that promises an uncertain outcome, while the authority of Spanish Prime Minister Mariano Rajoy has been dented by a party financing scandal.
"It's a balance of power that needs to be changed because otherwise Spain, Italy and France will be in even deeper difficulties, and that would be really problematic for the equilibrium of the euro zone," Waechter said.
Both Germany and France contracted last quarter, but business surveys this week have underscored how Europe's two largest economies are now growing apart.
France's all-industry business climate index for February was flat for the third month in a row, the state statistics office said on Wednesday, a day after Germany's ZEW sentiment index jumped to its highest level in nearly three years.
That tallied with a rise in Germany's Purchasing Managers' Index last month to 54.4, its highest level since June 2011. France's index dropped to 42.7, the lowest since March 2009.
Financial markets seem unperturbed. Yields on 10-year French bonds remain below 2.30 percent.
Nicholas Spiro with Spiro Sovereign Strategy, a London consultancy, said France is treated as a core euro member by the bond markets but, judged by many economic and structural indicators, it should be classed as a ‘lucky peripheral'.
"France's perceived creditworthiness is strong not because of fundamentals - which are shockingly bad in a number of areas and deteriorating by the day - but because investors do not have many options in terms of deep liquid and relatively safe bond markets as an alternative to Germany," he said.
Since the birth of the euro in 1999, growth in both France and Germany has averaged 1.4 percent a year, bang in line with the euro zone average.
In the period 1999-2007, France outperformed Germany. Since the crisis, however, France's economy has shrunk 0.1 percent a year on average, while Germany's has grown 0.8 percent, according to economists at JP Morgan.
Germany is reaping the benefits of a fall in its real exchange rate by 16.4 percent since 1999, achieved by dint of wage discipline.
By contrast, France's rate has risen 4.5 percent over the same period. That helps explains why France has lost a bigger share of global markets since 1999 than any other member country except for Italy and Greece, the bank said in a report.
On the budget front, Germany enjoys structural and primary budget surpluses, while France is in the red on both counts.
"France's fiscal, competitive, and structural challenges are substantial, and the economy looks to be taking a step down even as the rest of the region starts to move up," the bank said.
At the same time, the political relationship with Germany has become increasingly unbalanced in the latter's favour. "In the longer term, France has a difficult choice to make between the protection of the existing social model and its political influence within Europe," JP Morgan concluded.
TROUBLE AT THE CORE
France is not the only core euro member struggling to keep up with Germany. Finland contracted in 2012, hurt by weak exports and troubles at one-time telecoms growth engine Nokia.
The Netherlands is in recession as a depressed housing market saps confidence and consumption.
Given how closely entwined the Dutch and German economies were, the monthly sentiment index produced by the Ifo institute in Munich used to be a good leading indicator of Dutch jobs growth, according to economists at Jefferies in London.
But that relationship has all but broken down since 2010, partly because of the Netherlands' over-reliance on exports to an enfeebled euro zone. If the poor news flow continues, the Netherlands could lose its prized AAA credit rating in coming months, they said in a report.
So how might divergence give way to convergence at the core?
Normalisation of euro zone financial conditions will help. Because of a flight to the safety of German banks, lending rates for households and companies are about half a percentage point lower in Germany than they are in France and the Netherlands. That gap should close as banks gradually resume normal service.
Economists will also be looking for signs that reforms are working. The Netherlands is overhauling mortgage tax relief, while France has passed some labour reforms and given employers a 20 billion euro tax break to narrow the competitiveness gap with Germany.
But Spiro said the task facing Hollande remained immense.
"France is not making sufficient headway relative to the scale of the challenge. It's tinkering at the edges as far as reforms are concerned," he said.
(Reporting by Alan Wheatley, editing by Mike Peacock)