Lyon have threatened legal action following the decision to end the Ligue 1 season as a result of the coronavirus pandemic.
Paris Saint Germain have already begun celebrating a ninth title in their history, after the final standings were determined on a points-per-game played basis.
The final composition of the league left Lyon in 7th position.
They had been one-point off Reims and Nice in the race for Europa League football, and with a much healthier goal difference (+15).
Ending the season early had not been the wish of Lyon president Jean-Michel Aulas.
Earlier this week, he had proposed a three-stage playoff system, which would effectively decide European placings with a series of knockout ties.
In a statement, Lyon have also cited French sports minister Roxana Maracineanu, who left the door open earlier this week for a possible August conclusion to the 2019-20 season.
Lyon claim their legal action is based on the fact they have been denied "several tens of millions of euros".
Lyon's statement reads:
This government position did not seem to impose in a prohibitive way such a definitive stop today from Ligue 1 and Ligue 2, the Minister of Sports Roxana Maracineanu having previously indicated the possibility of playing in August if the evolution of the sanitary situation allowed it.
Olympique Lyonnais then proposed as early as Tuesday that the League study an alternative solution which would allow the Championship to be ended and thus preserve the fairness inherent in any sporting competition and to be in line with UEFA's proposals based on sporting merit according to objective, transparent and non-discriminatory principles.
This solution shared by other clubs was based on the principle of play-offs and play-downs, a title of champion acquired by PSG, with a calendar limited to 3 weeks consistent with health constraints, and an innovative formula which normally could have interested broadcasters, currently lacking content, as well as sports betting and all other economic players in the football industry. This solution made it possible very precisely to meet UEFA's wish to go after national competitions.
Given the judgment of the French Ligue 1 Championship, decreed today by the League, Olympique Lyonnais reserves the right to appeal against this decision and claim damages, in particular under the loss of chance and in light of the jurisprudence of other professional sports which are currently in progress, since the damage for the club amounts to several tens of millions of euros.
Olympique Lyonnais sincerely congratulates the champions, PSG for Ligue 1 and Lorient for Ligue 2, who were proclaimed today and hopes that OL Féminin can quickly have the same consecration.