His father, a professor of philosophy, gave him an education at the Stanislas College and the École Normale, where he graduated in 1848. After being professor of philosophy at several provincial universities, he received the degree of doctor, and came to Paris in 1858 as master of conferences at the École Normale.
In 1861, he became inspector of the Academy of Paris, in 1864 professor of philosophy to the Faculty of Letters, and in 1874 a member of the Académie française. He married Pauline Cassin, the author of the Pêche de Madeleine and other well-known novels.
In his philosophy, he was mainly concerned to defend Christianity against modern Positivism. The philosophy of Victor Cousin influenced him strongly, but his strength lay in exposition and criticism rather than in original thought.
Besides important contributions to La France and the Revue des deux mondes, he wrote Du mysticisme au XVIIIe siècle (1852–1854), L'Idée de Dieu (1864), Le Matérialisme et la science (1868), Le Pessimisme au XIX' siècle (1878), Jours d'épreuve (1872), M. Littré et le positivisme (1883), George Sand (1887), Mélanges et portraits (i888), La Philosophie de Goethe (2nd ed., 1880).