Brunel will step down from his role after this year's Rugby World Cup in Japan with the FFR still to appoint a successor, however, Laporte told French-Monégasque radio station RMC that Schmidt was his number one target if the referendum had passed.
Laporte responded to the clubs' decision, saying: "It's important for me to give the floor to the clubs". We have set up direct democracy and referendums to involve clubs in important decisions.
It comes after a referendum of the country's amateur rugby clubs ruled out a non-Frenchman taking charge.
"I will respect this choice", said federation head Bernard Laporte, who has made handing power back to the clubs the motif of his bid for re-election as FFR chief in 2020.
France will host the next World Cup in 2023 - with a French coach at Les Bleus' helm.
"The question of the French or foreign nationality of the coach of the XV of France is sometimes a debate for insiders and enthusiasts". To decide this, 59 per cent of the clubs do not to want a coach of foreign nationality. "We can move forward serenely to build the necessary conditions with the goal of winning the World Cup in 2023".
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Numerous foreign coaches, including Warren Gatland, Sir Clive Woodward, Vern Cotter and John Mitchell were reportedly on the French federations shortlist for the future position.
The current Crusaders coach has been linked as an option to join the French backroom team for the World Cup.
Schmidt, like Brunel, is finishing up with Ireland after the World Cup and has said he will return to New Zealand.
But, as the vote revealed, there was widespread hostility to the notion of France hiring its first overseas coach.
Everyone's in the Team Of Us.