The suspension applies to all matches controlled by the LFP, notably Ligue 1 and French League Cup fixtures.
The GoalControl technology failed to alert the referee to a Paris Saint Germain goal scored in their Amiens - it was instead awarded by the video assistant referee, which is now being trialled in France.
Didier Quillot, the league general director, said the service provided by GoalControl was not reliable at the moment, and hinted French football authorities could end the partnership.
The LFP said it will announce next week "follow-up action to be taken in relation to this dossier".
In Angers' clash with Montpellier on the same night, the referee's watch vibrated when there was no goal before he decided not to use the technology at all in the second half.
That contract is now in jeopardy, even with Ligue 1 having used GoalControl since 2015.
Goal-line technology entered football after a goal was wrongly disallowed at the 2010 World Cup.
VAR has especially been pushed by all corners and have begun to be used in various league and competitions.
Also, with major errors by referees in the La Liga sparking controversies, it is expected that the Spanish League will introduce VAR next season.
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