The clubs voted 59 per cent against a foreign coach replacing Jacques Brunel, whose contract expires at the end of this year's World Cup.
France, who have never been trained by a foreign coach and will host the 2023 World Cup, have slipped down to eighth in the World Rugby rankings and face an uphill task to advance from their 2019 World Cup Pool, which features England and Argentina.
Since Marc Lievremont took Les Bleus to the 2011 World Cup final, France have failed to live up to their reputation, finishing only once in the top three of the Six Nations.
"I will respect this choice," Laporte said in a statement.
Taking a foreign coach to get France back to the top had been raised as an option with the names of Warren Gatland and Eddie Jones being cited.
Laporte will announce the name of Brunel's successor before the World Cup starts in Japan on Sept. 20.
(Reporting by Julien Pretot; Editing by Christian Radnedge)
