French President François Hollande is expected to name interior minister Manuel Valls as his new prime minister, reports BBC News.
Mr Hollande's ruling Socialists are badly bruised after local elections which saw big gains for conservatives and the far-right National Front (FN).
Mr Valls is set to replace PM Jean-Marc Ayrault, whose office confirmed his resignation on Monday.
President Hollande, whose popularity has slumped, will address the nation at 20:00 local time (1800 GMT).
Opinion polls suggest that Mr Valls, 51, is popular - including among right-wing voters.
The second round of municipal elections on Sunday saw the Socialists lose more than 150 towns and cities of more than 9,000 inhabitants. Results are still being counted.
Read more of this report from BBC News.