Norbert Goeneutte was born in Paris, France, on July 23, 1854. He was enrolled in the prestigious Lycée Condorcet high school when the Franco-Prussian war broke out, followed by the Commune, and he was sent away for his protection. He finally graduated in 1871 and, despite an interest in art, was sent by his father to work for an attorney's office.

After his father's death shortly thereafter, he enrolled in the École des Beaux-arts to study under Isidore Pils. After Pils' death In 1875, and finding himself dissatisifed with the new professor, Goeneutte left the school to set up his own studio in Montmartre and immerse himself in the lively Paris art scene. Befriended by Édouard Manet, he was soon welcomed into the circle of Impressionists that frequented the famous Cafe de la Nouvelle Athènes, including Pissarro, Van Gogh, Degas, and Renoir, for whom he would model for several paintings.

Around 1875 he was introduced to intaglio printmaking by Marcellin Desboutin, and the medium would soon become as preferred as oils. He began exhibiting at the Paris Salon, gaining critical acclaim for the painting "The Boulevard de Clichy Under Snow" in 1876. Despite his association with Paris' most controversial and celebrated artists of the time, he chose not to participate in the major Impressionst exhibitions that would become landmarks of change, preferring instead the Salon's traditional venue. In 1889 he cofounded the Société des peintres-graveurs français along with Félix Braquemond and Henri Guérard.

Goeneutte traveled extensively, sketching the landscapes and street scenes of Italy, England, the Netherlands, and much of rural France. However in 1891 Goeneutte was diagnosed with a weak heart, possibly due to undetected tuberculosis, and was directed to end his travels and move to the countryside. His doctor, the artist and art patron Paul Gachet, found him a house near his own in Auvers-sur-Oise, where Goeneutte settled with his mother and siblings. There, he became acquainted with an artist's group headed by Charles-François Daubigny, and worked on a series of engraved illustrations for the periodical La Renaissance littéraire et artistique with Gachet. Goeneuette was working on illustrations for Émile Zola's book La Terre when he died on October 9, 1894 due to his prolonged illness.