Léon-Maxime Giran was born in Paris on 23 August 1867, the son of Languedoc peasant stock who had come north; he later contracted his names into the signature by which he is known. He trained in the studios of Eugène Carrière, Henri Gervex and Alfred Roll — an unusually varied grounding, taking in Carrière's brooding tonalism and the polished Salon naturalism of the other two — and began by exhibiting figure subjects and portraits. In the 1890s he turned decisively to landscape, and it is as a painter of the French countryside, and above all of the valley of the Oise, that he made his career.

He exhibited at the Société Nationale des Beaux-Arts and at the Salon des Indépendants, where he showed regularly among the Neo-Impressionists. In 1898 the Galerie Le Barc de Boutteville — the small, combative Paris dealer who had given early exhibitions to Maurice Denis, Émile Bernard, Bonnard, Signac, Luce and Toulouse-Lautrec — mounted a one-man show of his work, which places him squarely within the avant-garde of those years rather than at its edges.

Giran-Max took a studio at Neuville-sur-Oise and worked the river from Conflans-Sainte-Honorine up through Auvers-sur-Oise, living for a period at Le Valhermeil in the rue d'Ennery. This was crowded ground: Pissarro was at Éragny a few miles upstream until 1903, Van Gogh had died at Auvers in 1890, and Cézanne, Daubigny and Vlaminck all worked the same water. He also painted in Spain, in Brittany and in the Midi.

His manner moved across his career from a broadly Impressionist handling — vigorous in touch, sensitive in feeling, with a shimmering but carefully nuanced palette — towards a more deliberate Neo-Impressionism of divided colour. He died in Paris on 1 November 1927, and the Salon des Indépendants held a memorial tribute to him the following year.