The 2019-20 season was suspended with 10 matches remaining as part of the French government's steps to contain the spread of the novel coronavirus last month.
With some teams having played 27 matches and others 28, the French League (LFP) drew up the final standings according to a performance index -- number of points per game weighed by head-to-head record, resulting in Amiens and Toulouse going down.
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"It is an injustice because Amiens could not defend until the end on the pitch to remain in Ligue 1," 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.
"There will be the passage to the general assembly, and we reserve the right to go further so that justice passes."
Paris St Germain were awarded a seventh league title in eight years while seventh-placed Olympique Lyonnais, who missed out on European qualification, said they would possibly appeal against the LFP's decision.
The news comes as the Portuguese league said it could re-start as soon as May 30. Meanwhile, Premier League clubs are due to meet again on Friday to discuss Project Restart - their plan to resume matches.
A recent leaked recording of League One's Bristol Rovers' PFA delegate, Alex Rodman, suggested that the Premier League could include 23 teams next season if three teams were promoted to the league but none were relegated. Additional relegations could then be made across the top four leagues over the following seasons.
With regards to the Ligue 1 situation, French Sports Minister Roxana Maracineanu said the 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.
"The sports movement is autonomous... This is valid for professional sport and amateur sport alike. In this situation, there are some who are content and some who are dissatisfied.
"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 Aug. 22-23 at the latest and likely to be held without fans as popular events are banned until September in France.
French PM confirms Ligue 1 season cancelled, no football until September