The Portuguese boss was shown a red card by referee Benoit Millot for dissent in stoppage-time of their 2-1 win over Brest.
Fonseca was booked earlier in the match before seeing red, and now he looks set for a huge dugout suspension due to his reaction.
The 51-year-old is also set to be punished internally by Lyon for his antics.
According to L'Equipe, the club will hand out their own sanction to Fonseca as he awaits a possible Ligue 1 suspension.
Meanwhile, he has been summoned to face the league's disciplinary committee on Wednesday, the report adds.
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When Millot displayed the red card, the Lyon manager marched up to the official, squaring up and screaming in his face.
His furious rage falls under LFP's (French League governing body's) Article 8 regarding "intimidating or threatening behaviour."
The rulebook states that the outburst was "intimidating, all words, gesture and/or attitude that could inspire fear.
"Is threatening, all words, gesture and/or attitude expressing the idea of prejudice to the physical integrity of a person."
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According to the rules, any manager or club staff member found guilty of this towards an official can face a ban of up to seven months.
An article in French publication RMC Sport stated: "The LFP disciplinary committee must decide this Monday morning.
"But there is a good chance that Paulo Fonseca will be summoned this Wednesday and will know the length of his suspension immediately afterwards... the committee would like to move quickly and hit hard."
Lyon's players knew the dangers of their manager's reaction at the time, and they were quick to intervene, with some even pushing him away.
But Fonseca decided to turn around and make his way back towards Millot before members of his squad stood between the two before two apparent members of security helped lead him away.
Speaking to DAZN via RMC Sport after, Fonseca issued an apology for his behaviour that marred Lyon's home victory.
"I apologise for this gesture," he said. "I shouldn't do that. Football makes us do bad gestures. The match was very difficult.
"Playing against Brest is always difficult, they are a physical team, they defended a lot. These are very important points."
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Lyon captain Alexandre Lacazette also said: "It's part of football.
"I think he'll regret this gesture, but we'll see what the disciplinary committee says.
"It's tension. There are a lot of questionable choices. When you live the match, sometimes you can do things. We're all behind the coach."
Fonseca, a former centre-back, started the 2024/25 season as the head coach at AC Milan.
However, he spent just six months at the San Siro and left the club eighth in Serie A at the end of December.
The 51-year-old was appointed at Lyon a month later, which sealed his return to Ligue 1 following a previous spell with Lille.
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Victory against Brest was his third from five matches since completing his move and has them sitting sixth in the French top flight.
Lyon next face Romanian outfit FC Steaua Bucuresti in the Europa League on Thursday before a league clash at Nice, although Fonseca is set to be absent through his suspension.