In Germany, Europe's economic powerhouse, gross domestic product (GDP) expanded by 0.1 percent in the period from July to September, after shrinking by 0.1 percent in the preceding three months, the federal statistics office said.
And in Paris, a preliminary estimate by the INSEE agency showed the French economy grew by 0.3 percent in the third quarter, following a contraction of 0.1 percent in the second quarter.
Since recession is technically defined as two consecutive quarters of falling GDP, both France and Germany avoided a new recession.
In Germany's case, positive impulses came primarily from private households, which ramped up their spending strongly, Destatis said.
In addition, foreign trade also provided a support for the economy, with exports rising more strongly than imports, the statement said.
On the negative side, investment declined, particularly in equipment, and construction investment also slipped marginally.
A detailed breakdown of the different GDP components will be published on November 25th, Destatis said.
In Paris, France's Finance Minister Michel Sapin said the French data confirmed the government's forecast of 0.4 percent growth for the full year.
"Economic activity has picked up slightly but remains too weak to ensure the job creation our country needs," Sapin said in a statement.
With growth in both countries still very modest, however, analysts were cautious about the outlook.
"Almost all the glamour of the second German 'Wirtschaftswunder' (economic miracle) seems to be gone," said ING DiBa economist Carsten Brzeski.
Data for the wider eurozone was scheduled for release later on Friday and the chances are that it will show that Germany underperformed in comparison with the rest of the region, the expert said.
"Since early 2013 the German economy has grown by an average of 0.2 percent quarter-on-quarter each quarter, making the eurozone's powerhouse rather a one-eyed king in the land of the blind than an economic superman," he said.
Brzeski attributed the German weakness to problems in key trading partner countries such as China, France and Italy. But uncertainty stemming from the ongoing Ukrainian crisis was also another key factor, he said.
"In our view, the German economy is nowhere near any abyss. However, complacency or any trace of high-handedness would be misplaced. The trend of the last quarters signals that the German economy could use a new reform impulse rather sooner than later," he concluded.