Galthie played 64 times for France and captained the side to a Six Nations Grand Slam in 2002 and also led them at the 2003 World Cup.
Brunel's contract expires at the end of the World Cup and amateur clubs had voted against the idea of bringing in a foreign coach in a referendum initiated by Laporte earlier this month.
The Rugby World Cup begins on Sept. 20 in Japan and France begin their campaign a day later against Argentina in Pool C.
(Reporting by Rohith Nair in Bengaluru; Editing by Toby Davis)
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