Lyon have threatened legal action after they missed out on the European spots when the Ligue 1 season was ended.
Rudi Garcia's side have been placed seventh after the campaign was cut short by 12 fixtures because of the coronavirus pandemic.
It has seen them fail to qualify for Europe, despite being one point behind sixth-place Nice, which the club claims could cost them tens of millions of Euros.
Paris Saint-Germain, meanwhile, were handed a ninth Ligue 1 title.
In a statement on Lyon's website, a club official said: "Olympique Lyonnais has taken note of the decision proposed by the Office of the Professional Football League and endorsed this afternoon then by its Board of Directors, to end the 2019/20 season of Ligue 1 and Ligue 2, based on the remarks made by Prime Minister Edouard Philippe during his speech at the National Assembly on the conditions of deconfinement.
"This government position did not seem to impose in a prohibitive way such a final 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 health 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 Feminin can quickly have the same consecration."