[2] Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg, was one of the three co-founders of modern triangle geometry.

[4] He spent most of his life studying meteorology as an officer in the French Navy, but seems to have made no notable original contributions to the subject.

After graduating from the Lycée he entered the Academy in Strasbourg where he was prepared for the examination for entrance to the prestigious École Polytechnique in Paris, to which he was accepted in 1865.

Brocard was one of the 120,000 men under Marshal MacMahon led to Metz to free the French army of the Rhine.

His remaining two major publications were Notes de bibliographie des courbes géométriques (1897, 1899, published in two volumes)[5][10] and the Courbes géométriques remarquables (1920, posthumous 1967, also published in two volumes) which was written in collaboration with Timoléon Lemoyne.

[11] Brocard attended the International Congress of Mathematicians at Zurich in 1897, Paris in 1900, Heidelberg in 1904, Rome in 1908, Cambridge, England in 1912, and Strasbourg in 1920.

He was offered the presidency of Bar-le-Duc's Letters, Sciences, and Arts Society, of which he had been a longtime member and correspondent for several foreign academies of, but declined.

In his paper Analyse d'autographes et autres écrits de Girard Desargues, he surmised that it stood for Des Argues, Lyonnais, Géometre, which is the generally accepted title.