"Financially the Germans drive a lot of what goes on, because they're the biggest economy in Europe, but politically they know they need the French to work with them," Al Jazeera's Alan Fisher, reporting from Brussels, said.
"And over the last few days we've heard the French saying different things than the Germans."
The day-long meeting, the second this week, is expected to conclude with a press conference on Friday afternoon.
Ongoing concerns about the euro, coupled with fears about the economic recovery in the US, drove stock markets in Europe and Asia lower on Friday.
Germany's DAX and the UK's FTSE 100 both opened down, losing roughly 1 per cent of their value in early trading.
In Asia, the Nikkei - Japan's benchmark index - closed down roughly 2.5 per cent in trading on Friday, bringing the index to a five-year low.
Taiwan's stock exchange slipped 2.5 per cent; Shanghai's main index was down more than half a per cent in the morning, though it regained ground in afternoon trading.
The poor early showing in Europe and Asia follows a rough day of trading in the United States. US markets fell sharply on Thursday, with the Dow Jones Industrial Average sliding 3.6 per cent.
The numbers partly reflect an unexpected jump in jobless claimsin the United States.
The US labour department said on Thursday that 471,000 people applied for unemployment benefits in the week ending May 15. That was a 5.6 per cent increase from the prior week's total.
Analysts had expected the number of jobless claims to drop. Investors fear the poor showing is a bad sign for the US economic recovery.
"People believed the recovery was underway, they anticipated continuous improvements in the unemployment rate," said Steve Keen, an economics professor at the University of Western Sydney.
"But the cause of this crisis too much debt, and we still have that debt overhang... that is depressing spending," which leads to continued high levels of unemployment, he said.