The figure, a rise of 216,100 over 12 months, had been largely expected but the announcement of the figure added to an accumulation of bad news surrounding the French economy as the franc came under renewed pressure expected to force a devaluation of the currency.
The June jobless figure represented a 1.4 per cent rise over May.
With the school and university year ending in July, the figure is certain to rise still further over the next two months. The most pessimistic forecasts put the likely figure for the end of the year at around 3.4 million unemployed.
The unemployment figure passed the three million mark just before last March's parliamentary elections which brought the conservative government headed by the Gaullist Edouard Balladur to power.
The previous Socialist government led by Pierre Beregovoy, who committed suicide on 1 May, had made it a point of honour to do all it could not to let the figure go above three million during its tenure.
While the unemployment figure was as bad as expected, other figures released yesterday showed that France had a foreign trade surplus of Fr7.65bn ( pounds 878.5m) in April, Fr550m up on the previous month.
Such is the current taste for gloom and doom among French analysts, however, that this result was largely seen as a reflection of a consumer slump which had principally hit purchases of imported goods.
French exports fell to Fr91.24bn in April from Fr93.78bn in March as imports dropped to Fr83.59bn from Fr86.33bn.
The agricultural trade surplus rose to Fr4.5bn from Fr3.4bn.
But the industrial goods surplus, including military sales, dropped to Fr5.6bn from Fr6.6bn the previous month.