Federation Internationale de Football Association said in a statement last month that it has yet to confirm whether GoalControl will be used in Russia for this year's World Cup, according to the Associated Press.
During this week's Coupe de la Ligue quarter-finals, errors were made by the GoalControl system on two separate occasions.
France is also trialling the video assistant referee (VAR) system in the League Cup - from the quarter-finals onwards - with a view to introducing it in Ligue 1 next season.
The French league already said last month it wanted improvements after expressing "dissatisfaction with the failures" in several matches with GoalControl, the same system used at the 2014 World Cup.
With the recent errors, LFP took the decision to suspend the technology.
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There was also a mistake during Angers v Montpellier.
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.
That contract is now in jeopardy, even with Ligue 1 having used GoalControl since 2015. The Premier League uses the Hawk-Eye system since 2013-14, which has largely been controversy free.
Report says Goal Control is one of four licensed providers of goal line technology, approved by world football governing body FIFA.
VAR has especially been pushed by all corners and have begun to be used in various league and competitions.
The technology and VAR were provided by Hawk-Eye at the Confederations Cup previous year.