Blatter: France must not meddle in football
Blatter's threat came a day after French Football Federation (FFF) president Jean-Pierre Escalettes resigned in the wake of France's World Cup fiasco.
French Sports Minister Roselyne Bachelot had said last week Escalettes's resignation was "unavoidable".
"In France they have made an 'affaire d'Etat' with football, but football remains in the hands of the federation," Blatter told reporters on Tuesday.
"French football can rely on FIFA in case of political interference even if it is at presidential level, it is a clear message.
"We will help the national association and if cannot be solved by consultation then the only thing we have is to suspend the federation."
France's group stage exit, marred by the players' decision to boycott a training session in support of expelled striker Nicolas Anelka, has sparked soul-searching and high-level meetings in the country.
Such was the national angst in France that President Nicolas Sarkozy urged a football shakeup and met former team captain Thierry Henry.
The debate will continue with the news on Tuesday that both coach Raymond Domenech and Escalettes would be heard by a parliamentary commission of the National Assembly on Wednesday.
The players' boycott came after Anelka was kicked out of the squad by the FFF for insulting Domenech at half time of a 2-0 defeat by Mexico.
France ended bottom of Group A with a draw and two defeats. Domenech will be replaced by Laurent Blanc.