Guy Noves retains the support of French Rugby Federation president Bernard Laporte, but must oversee improvement later this year following a 3-0 series defeat to South Africa.
This month's whitewashing at the hands of the Springboks followed a Six Nations campaign that saw France finish third, winning three matches and losing two.
Laporte - a former national coach himself - has now set France the target of winning three of their four November internationals in order to boost their lowly world ranking.
Les Bleus are due to face New Zealand, South Africa and Japan, with a second match against the All Blacks also in the offing.
Asked by Le Parisien if he still has faith in Noves, Laporte replied: "Yes, of course. The players, Guy and I - we are all in the same boat. I'm with them.
"The truth is this [France's poor run] can no longer be tolerated. In November, we need to win three games of the four we'll play.
"The main goal is crystal clear. It doesn't mean that if we cannot achieve it some people will be sacked. We must have that goal in mind, however.
"I cannot accept the fact that we are the eighth nation in the world. I support Guy Noves and together we must bounce back."
Former Toulouse coach Noves took the job in 2015 as successor to Philippe Saint-Andre.