Jean-Marc Ayrault stepped down as prime minister after acknowledging that he and his cabinet ministers bore the blame for Sunday’s defeat, which saw 155 towns swing to the centre-right UMP and the far-right Front Nationale claim 11.
Mr Hollande named interior minister Manuel Valls, 51, as the new prime minister in a TV address last night.
However, it could be several days before a new cabinet is announced.
France has lived with an unemployment rate of around 10 per cent for several years and polls show the public do not trust the government to cut it. Facing the lowest popularity levels of any president in France’s 56-year-old Fifth Republic, the Socialist Party changed tack earlier this year towards a more pro-business stance aimed at spurring investment and jobs through corporate charge cuts.
Mr Hollande has said the mid-April vote in parliament on the “responsibility pact” package of €30 billion (about £24.7bn) of cuts is a vote of confidence in his government.
But left-wingers said the move to the right had not worked, and working-class voters wanted Mr Hollande to return to his Socialist roots.
“Don’t be afraid to abandon this path,” said an open letter to Mr Hollande posted on the website of Paris Socialist senator Marie-Noelle Lienemann and signed by left-wingers Jerome Guedj and Emmanuel Maurel.
“Job creation comes from a re-launch of public investment and consumption,” it said, urging Mr Hollande to end a freeze on public sector salaries, raise the minimum salary and pensions.
Provisional results from Sunday’s voting showed the anti-EU Front Nationale party of Marine Le Pen taking control of 11 towns across the country plus one district in Marseille, a new record for the party. “Punishment” read a front-page headline in the left-leaning Liberation newspaper.
However, Socialists retained control of Paris city hall, with Anne Hidalgo due to become the city’s first female mayor.
The Front Nationale’s wins were largely in the south, which has a tradition of anti-immigrant feeling. But it also took power in northern towns such as Henin-Beaumont and Hayange, which are suffering from France’s industrial decline.
“This result is proof that we can win on a grand scale,” Ms Le Pen told BFM TV, adding that the vote showed her party could win European Parliament elections due in late May.
Pollsters Ipsos put the Front Nationale narrowly behind the UMP – the party of ex-premier Nicolas Sarkozy – for the EU vote, with the Socialists third.