In estimates released late Thursday, the INSEE national statistics office said the economy would grow by 0.4 percent in the first quarter of the year and by 0.3 percent in the second.
The forecasts suggest there is a good chance the French economy will grow faster over the whole year than the 1.0 percent Paris currently estimates.
"The one-percent for 2015, seen by many as unrealistic a few months ago, now looks like the minimum," said Finance Minister Michel Sapin.
However, the more positive growth outlook will be insufficient to drive down stubbornly high unemployment in France, INSEE predicted.
The jobless rate was forecast to hit a 20-year record high of 10.2 percent in mainland France.
Economists and the government estimate that a growth rate of around 1.5 percent annually is required to push unemployment down.
President Francois Hollande has pledged not to seek re-election in 2017 if he does not succeed in reversing the trend of increasingly high unemployment.
"Our economy is starting up again," Hollande said in a speech about the economy on Friday.
"The figures published this morning confirm that. But it is starting up too slowly. We are talking about a growth rate of more than one percent in 2015," said the president.
"But we should have bigger ambitions and we need more than one percent growth to create jobs," he said.