Plaintiffs identified only as Corinne C. et Sophie H. had contended that Articles 75 and 144 of the Code Civil (in English here) -- each of which designates that the couple to be married will be compsed of a man and a woman -- denied them rights and liberties guaranteed by the French Constitution.
Invoked was Article 6 of the 1789 Declaration of the Rights of Man and the Citizen (available here in the original French), which, in English translation, sets out the principle of equality:
Law is the expression of the general will. Every citizen has a right to participate personally, or through his representative, in its foundation. It must be the same for all, whether it protects or punishes. All citizens, being equal in the eyes of the law, are equally eligible to all dignities and to all public positions and occupations, according to their abilities, and without distinction except that of their virtues and talents.The 6-man, 2-woman Conseil (prior posts here, here, and here) articulated as its basis for sustaining the ban on same-sex marriage a structural / separation-of-powers / judicial restraint argument. It's an argument that American constitutionalists will find rather familiar.
Pivotal was ¶9 of the 11-paragraph judgment styled Mme Corinne C. et autre [Interdiction du mariage entre personnes de même sexe]. Per loose translation by this 'Grrl, ¶9 repeated the gist of Article 6 quoted above, then continued with additional considerations:
With that, it would seem, French marriage-equality advocates must move chez le Parlement.
► The principle of equality is not contravened by legislation that regulates different situations in different fashions, nor by certain inequalities adopted in the general interest, provided that the resulting difference in treatment bears a direct relationship to the goal underlying the legislation;
► In maintaining the principle according to which marriage is the union of a man and a woman, the legislature, exercising power granted by Article 34 of the Constitution, has deemed that the difference of situation between same-sex and opposite-sex couples can justify different family law rules;
► It is not for the Conseil constitutionnel to substitute its judgment for that of the legislator respecting the nature of this difference of situation;
► For these reasons, the complaint is dismissed.