The 54-year old sought refuge in the South African embassy in Bujumbura, Burundi, earlier this month when he found out he was wanted by Congolese authorities.
The DRC accuses Lumbala of having links with the rebel movement M23 and supporting a rebellion in eastern Congo, displacing at least 220,000 people within six months.
His lawyer, Prosper Niyoyankana, confirmed Lumbala flew out of Burundi on Saturday and is due to arrive in France on Sunday.
A spokesman for the Congolese government, Lambert Mende, says the DRC will ask France to extradite Lumbala.
Lumbada’s move “doesn’t change the gravity of the facts that out country has against Mr Lumbada,” Mende said.
“This simply means that we are going to orientate our extradition demand towards France, and [not] towards South Africa or Burundi,” he added.
“It is still about the millions of lives that this rebellion has cost this country, and we want to fight against impunity. Therefore being in France doesn’t put Lumbala above judicial procedures [for extradition],” Mende stressed.
The United Nations allege M23 is supported by Rwanda, which the country denies.
The rights group Human Rights Watch says M23 is responsible for war crimes and gross human rights violations, including summary executions, rape and forceful recruitment of soldiers.
Its alleged leader, Bosco Ntaganda, is wanted by the International Criminal Court for war crimes and recruiting child soldiers.
Lumbala has led the Rally of Congolese Democrats and Nationalists since 2000.
The rebel movement transformed into a political party in 2003, and Lumbala stood for presidential elections in 2006.