French club Lyon have said they will seek damages for a "big loss of opportunity" after the Ligue 1 season was cancelled due to the coronavirus pandemic.
Lyon were denied a spot in a European competition for the first time in a quarter of a century following the French League's decision.
Amiens, who were relegated along with Toulouse after the season was abandoned, are also considering legal action.
With some teams having played 27 matches and others 28, the French League (LFP) drew up the final standings according to a performance index.
This saw the number of points per game weighed by head-to-head record, resulting in Lyon finishing seventh with no chance of a European spot for 2020-2021.
"It's a big loss of opportunity that has a financial value that amounts to dozens of million euros, which will be claimed in damages," said Lyon president Jean-Michel Aulas, whose club won the Ligue 1 title from 2002-08 and reached the Champions League last four in 2010, told local newspaper Le Progres.
Aulas argued the season could have been finished in the form of play-offs behind closed doors in August and that the ranking method was disputable.
"We see that these standings are illogical. I don't want to single out a club more than another but Nice played at home more than us and faced Paris Saint-Germain only once while we played them twice," he said.
"Over the last 10 years, [Lyon] caught up at least three times with the second-placed team while lagging more than 10 points behind."
Lyon were seventh after 28 games on 40 points, 10 behind third-placed Stade Rennais, who occupy the last European Champions League qualifying spot.
PSG were awarded the title with second-placed Marseille securing a direct access to the Champions League group phase.
Lyon, who have featured in a European competition every season since 1995-96, are still in this year's Champions League.
They beat Juventus 1-0 in the first leg of their last-16 tie and could still play in the competition next season if they win it this year, should it be completed.
Amiens, who were relegated along with Toulouse, said they would study the reasons behind the decision before planning any legal challenge.
"It is an injustice," Amiens president Bernard Joannin said in a Facebook live broadcast.
"I'll fight with all the teams to assert our right, because I think this decision isn't right. We will wait for the minutes of the LFP board of directors."
French Sports Minister Roxana Maracineanu said aggrieved clubs were welcome to explore legal options but also called for restraint.
"If they want to go to court, let them go," Maracineanu told RMC Sport. "I appeal to everyone's solidarity and responsibility. I appeal to the wealthy and better off that they don't split hairs ... We must also think of others and society. The world must know how to take its losses."
The new season will start on August 22-23 at the latest and is likely to be held without fans as mass gatherings are banned in France until September.