Lieutenant DeSalle was a Human male of French descent. He served as a Starfleet officer in the mid-23rd century. He was assigned aboard the USS Enterprise under Captain James T. Kirk, during a historic five-year mission that starship undertook. In 2267, he served in the command division as one of the ship's navigators. Later the same year, he transferred to the operations division, where he became an assistant chief engineer in the engineering department.
During that time, on stardate 2124, DeSalle was one of three people who beamed down to the planet Gothos in search of Captain Kirk and Lieutenant Sulu, who had been abducted by Trelane, a powerful alien. Expecting to arrive in an inhospitable climate, this landing party was surprised to discover an oasis of Earth-like conditions. When communications failed, DeSalle attempted to contact the ship using a laser beacon, but this method also failed. DeSalle later attempted to shoot Trelane with his phaser, but Trelane momentarily paralyzed DeSalle, procured the phaser and delightedly experimented with it, disintegrating several bizarre trophies he owned, before returning the weapon. (TOS: "The Squire of Gothos")
Later that year, on stardate 3417, DeSalle accompanied Captain Kirk on a landing party to the Omicron colony, on Omicron Ceti III. DeSalle discovered that, anomalously, the colonists themselves had been the only animal beings to survive exposure to the planet's berthold rays. He also performed an analysis on crops grown by the colonists. Like the rest of the Enterprise crew, DeSalle fell under the influence of the Omicron spores and mutinied, though he later recovered, thanks to a subsonic transmitter. (TOS: "This Side of Paradise")
On stardate 3018, DeSalle was placed in command of the Enterprise while the rest of the senior staff (including the captain, first officer, chief engineer, and the helmsman) were off the ship, and spearheaded an effort to pierce an alien barrier, which had been erected by Korob to prevent the Enterprise from sending help to a landing party that was trapped on Pyris VII. The Enterprise crew were close to escaping the field when Korob removed it himself, as part of his effort to help the Starfleet explorers escape Sylvia's attention. (TOS: "Catspaw")
Background information Edit
DeSalle was played by actor Michael Barrier.
DeSalle's first name is not established on-screen but was given as "Vincent" in a cast list that was written for the final draft script of "The Squire of Gothos", dated 26 October 1966. The main body of the script described the character as follows: "Navigator Vincent De Salle – a tall, strong featured man." He was also listed as having that first name in Bjo Trimble's Star Trek Concordance; Trimble directly used many of the episode scripts in compiling her work. The FASA Cadet's Orientation Sourcebook remained true to the given name "Vincent" as well.
The script of "This Side of Paradise" referred to the character as "Lieutenant Timothy Fletcher". However, when Michael Barrier was cast in the role, the production staff realized he had previously played a character named "DeSalle" in "The Squire of Gothos", and changed the name accordingly. This explains why DeSalle was a navigator in the earlier episode, while he is a science officer in the later installment (and yet still wearing a gold uniform). 
DeSalle's promotion to assistant chief engineer and his change in uniform color in "Catspaw" was devised by Gene Coon. Since Scotty was in command of the bridge whenever both Kirk and Spock were on an away mission, Coon figured they would need someone in charge of engineering during these occasions. He intended to make DeSalle a recurring character. However, as incoming scripts didn't feature any interaction between the bridge and main engineering in such situations, this was finally abandoned. (These Are the Voyages: TOS Season Two)
His mirror universe counterpart appears in the novel The Sorrows of Empire. He succeeded Montgomery Scott as the chief engineer of the ISS Enterprise when Scott became Spock's first officer in 2267. The novel gave the mirror DeSalle's first name as "Michael".
In the novel Forgotten History, the prime universe DeSalle was named "Vincent M. DeSalle", in an attempt to explain why his mirror universe counterpart was called "Michael".