Henri Désiré Gauquié was born in Flers-lez-Lille on 22 October 1858. He initially studied art at the Academy of Valenciennes under René Fache. After competing in Lille, he obtained a scholarship to study at the Paris School of Fine Art at the studio of Jules Cavelier. He started exhibiting at the Paris Salon from 1881. In 1886, he won a third class medal and a travel grant from the Ministry of Public Instruction and Fine Arts for his group ‘Perseus, Vanquisher of Medusa'. This was later purchased by the State for the museum of Agen. After spending time in Italy and Belgium, Gauquié returned to France. He went on to win several other medals at the Salon including second prize in 1890 for his sculpture of Brennus and first prize in 1895 for his marble group Bacchante and Satyr , now owned by the city of Tourcoing. He also won a bronze medal at the L’Exposition Universelle in 1889, and a silver medal in 1900. In the same year he was appointed knight of the Legion of Honour and promoted to the rank of Officer of the Order of Academic Palms.

He produced several public monuments in collaboration with the architect Henri Guillaume dedicated to public figures such as Alexandre Le Grand, Jules Pean and Antoine Watteau as well as war memorials. Many of his monuments including those In Paris, Lyon, Rouen Cathedral and Fecamp are still standing today.
He died in Paris in 1927 and is buried at the Père-Lachaise cemetery.

Examples of his smaller sculptures can be found in a number of museums in France including Denain, Chartreuse, Reims, Tourcoing and Valenciennes.