Édouard joined the École Navale in 1973.[2] As an Enseigne de vaisseau (vessel Ensign), he first served on the patroller La Paimpolaise from 1976 to 1978, monitoring the nuclear trials in Mururoa.[3] Afterwards, he served consecutively for one year on two French nuclear ballistic missile submarinesSNLEL'Indomptable and Le Redoutable, following which he took command in 1979 of the minesweeper Lobelia, for another year until 1980. The next year, he studied for a specialisation in gunnery and missiles.
In the early 1980s, Guillaud was sent in exchange in the United States (U.S.). As a Lieutenant de Vaisseau (Lieutenant) from 1981 to 1984, he then served as service chief on the avisoAmyot d'Inville and the squadronescorteurs launch missile Du Chayla, then as a service operations chief on the squadron escorteur launch missile Kersaint, cruising off the seas between Iran and Lebanon in 1983.[2][3]
Guillaud went on to study at the Superior Naval War School (French: École Supérieure de Guerre Navale, ESGN) and the School of Military Application for Atomic Energy (French: École des Applications Militaires de l'Energie Atomique, EAMEA), rising to Capitaine de frégate in 1989.[2] He specialised in nuclear engineering, obtaining a degree in 1990.[2]
In 1991, with the start of the Gulf War, Guillaud was sent on the Clemenceau, where he served as a Maneuver Officer.[2]
In 1992, he took command of the aviso-escort Enseigne de vaisseau Henry (F749). In 1993, he re-integrated the design team for the nuclear carrier. Guillaud was promoted to Capitaine de vaisseau in 1996. The following year, he took the position of second officer on the Charles De Gaulle, which was then being completed in Brest.[2]
Since 19 March 2011, he has commanded the French forces enforcing the Libyan no-fly zone.[6]
In 2013 he commanded the French Forces in the Mali Civil War.
He left active duty service on 14 February 2014 when général Pierre de Villiers succeeded him at head of the armies. He assumed a French armament directorate until 2017.