The INSEE national statistics office had been predicting only 0.4 percent growth in gross domestic product (GDP) as late as last month.
The encouraging figures for the second-largest economy in the eurozone were welcomed as "clearly comforting" by Finance Minister Michel Sapin.
However the growth figure for the final quarter of last year was revised down by 0.1 points to zero growth.
The first quarter growth figure was driven by an 0.8 percent increase in domestic consumption after weak 0.1 percent growth at the end of 2014.
Investment continued to be a drag on the French economy, falling by 0.2 percent in the first quarter following a drop of 0.4 percent in the final quarter of 2014.
The figures suggest there is a good chance the French economy will grow faster over the whole year than the 1.0 percent Paris currently estimates.
"This first figure is very encouraging," Sapin told reporters. "Our growth perspectives for 2015 are today clearly comforting."
Last month he argued that France's predicted one-percent growth over the whole year which some saw "as unrealistic a few months ago, now looks like the minimum."
The German economy, Europe's biggest, grew by just 0.3 percent in the first quarter of 2015, slightly slower than expected, data published by the federal statistics office Destatis showed on Wednesday.
German analysts were disappointed, since they had been pencilling in first-quarter growth of 0.5 percent after GDP expanded by 0.7 percent in the fourth quarter of 2014.