The decision covers all matches under the jurisdiction of the LFP, notably Ligue 1 and the French League Cup, and comes in the wake of two errors during Wednesday's League Cup quarter-finals.
As a result of the failures of the system, the LFP announced on Thursday that the technology would be removed as a precautionary measure.
The referees overseeing Paris Saint-Germain's win at Amiens and Angers vs. Montpellier did not receive alerts on their smartwatches when the ball crossed the line, as was supposed to happen.
GoalControl was used at the 2014 World Cup, but the Premier League, Bundesliga and Serie A all use Hawk-Eye's technology.
Adrien Rabiot headed in the second goal but the referee's watch, which normally vibrates to indicate a goal, did not work, and he had to consult with video assistant referees to validate the goal.
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"We are going to look at what is available on the market", Quillot said.
Goal-line technology entered football after a goal was wrongly disallowed at the 2010 World Cup.
It was subsequently given after consultation with a Video Assistant Referee, which the LFP, like the FA, is also trialling.
The technology and VAR were provided by Hawk-Eye at the Confederations Cup past year.
The suspension by LFP is temporary and their statement added that an adminitrative council will meet next week to decide further action regarding GoalControl.