The Daily Telegraph reported Ecology Minister Jean-Louis Borloo, passed over as prime minister, said he had "decided not to be part of the next government." The British newspaper said Borloo could wind up running for president in 2012.
The Telegraph said the new, smaller Cabinet reveals a shift to the right side of the political spectrum.
Labor Minister Eric Woerth also is gone, as are Foreign Minister Bernard Kouchner, a Socialist, Sports Minister Rama Yade, the only black in the Cabinet, and Urban Affairs Minister Fadela Amara.
The new government will include Alain Juppe, a right wing former prime minister, as defense minister, replacing Herve Morin.
Michele-Alliot Marie takes over the Foreign Ministry from justice and Eric Besson, moves from the Immigration Ministry to industry.
Finance Minister Christine Lagarde and Culture Minister Frederic Mitterrand will stay on in their current roles.
Morin, also a possible presidential candidate who leads the center-right Nouveau Centre party, called the new governing body a right-wing "campaign team" where he didn't belong.
"France needs pluralism, and democracy needs balance. Since April 2010 the head of state has not agreed with this proposition, and so for my part I can't remain in government," Morin said.