"The superior appeal commission has decided to cancel the three-point penalty, including one suspended, handed to Monaco by the League disciplinary body after the club appealed the ruling," the FFF said in a statement.
Fireworks were set off during Monaco's last home game against Le Mans in May before fans invaded the pitch after the final whistle. In the melee, a referee was struck by a fan, according to the match official's report.
Monaco were also told to play one match behind closed doors, a sanction the FFF commission upheld.
It was not clear when this sanction would be enforced after the club brought the case to the French Sports and Olympic Committee (CNOSF), the highest national sporting authority.
They host Montpellier on Sunday in their second Ligue 1 match of the season after they beat Girondins Bordeaux 2-0 in their opener last weekend.
Big-spending Monaco, owned by Russian billionaire Dmitry Rybolovlev, are widely regarded as the main challengers to champions Paris St Germain this season.
They have splashed out around 150 million euros (£129 million) in transfers to sign Colombian striker Radamel Falcao, fellow countryman James Rodriguez and Portugal midfielder Joao Moutinho.