The headline total is bad news for the government on the opening day of the G20 summit in Saint-Petersburg, Russia, largely on the world economy, but there are signs that the upward trend may be easing.
The unemployment rate for young people fell from the first-quarter level while remaining high at 24.6 percent, the figures from the national statistics agency INSEE showed.
The data showed that the number of people without work rose above 3.0 million for the first time, but the labour minister said that he was pleased with the slowing trend.
In the first quarter, the rate had risen sharply by 0.3 percentage points.
The high level of young people without work is a particular concern for the left-wing government which is focusing on raising competitiveness and reducing unemployment.
The unemployment trend also has a direct impact on the outlook for growth since the extent to which people are concerned about jobs has a big effect on household spending, a vital driver of activity in France.
President Francois Hollande promised in July to reverse the rising trend of unemployment by the end of the year, saying that economic recovery was on the doorstep, but this was ridiculed by many economists at the time.
Since then, France has emerged from recession in the second quarter of the year and some indicators suggest that activity is picking up.
However, economists warn that the second-quarter rise of activity was driven mainly by bad weather and spending on energy.
Labour Minister Michel Sapin said that he was pleased that the rise of unemployment was "more moderate" than the increase in the previous quarter.
He said that the state of the labour market was "improving" and that the government's policies for the economy and employment were working.
The figure concerned only unemployment in mainland France. When overseas territories were included, the unemployment rate rose by 0.1 percentage points to 10.9 percent.
The total number of unemployed on the mainland rose above 3.0 million, and by 0.7 percentage points over 12 months on the basis of a calculation using International Labour Organization standards.
The INSEE data for the mainland showed that unemployment among people aged 15-24, which had reached a record rate of 25.5 percent at the end of 2012, fell by 0.6 points in the first quarter and by 0.3 points in the second quarter to 24.6 percent.