Dédé was the fourth generation of a free New Orleans family. His father was a marketman, poutry dealer, and music teacher. As a boy, Dédé first learned the clarinet, but soon switched to the violin, on which he was considered a prodigy. He would later go on to perform compositions of his own as well as those by Rodolphe Kreutzer, a favored composer of his. Dédé's teachers in his youth included violinists Constantin Debergue and Italian-born Ludovico Gabici, who was the director of the St. Charles Theater Orchestra. He was taught music theory by Eugène Prévost and New York-born black musician Charles-Richard Lambert, the father of Sidney and Charles Lucien Lambert.
Dédé's instruction from Gabici ended when he left to seek work in Mexico at the end of the U.S.-Mexican War in 1848. When he eventually returned to the US at the end of 1852, he worked as a cigar maker, saving money to be able to travel to Europe. He went first to Paris and then Belgium, where he helped his friend Joseph Tinchant set up a branch of the Tinchant family's cigar business. He returned to Paris around 1857 and became an auditeur at the Paris Conservatoire. He studied at the Conservatoire with Jean Delphin Alard and Fromental Halevy.
In 1864 Dédé married a Frenchwoman, Sylvie Leflet, and settled in Bordeaux. They had one son, Eugene Arcade Dédé, who became a music hall conductor and composer of popular songs.
In the early 1860s, Edmond Dédé went to Bordeaux to take up a position as assistant conductor for the ballet at the Grand Théâtre. Within a few years, he found employment at the Théâtre l'Alcazar, a popular café-concert in the city. Later in the 1870s, he moved to the Folies Bordelaises. Throughout Dédé continued to compose art music, which he sought to have performed at the more prestigious Grand Théâtre.
Samuel Snaer, Jr. (1835–1900), an African-American conductor and musician, conducted the first performance in New Orleans of Dédé's Quasimodo Symphony. It was premiered on the night of May 10, 1865, in the New Orleans Theater to a large audience of prominent free people of color of New Orleans and Northern whites. Dédé was not present at this performance.