In July 1684 Minet, of whom virtually no personal details are known, sailed from France with Réné Robert Cavelier, Sieur de La Salle, to plant a French colony on the lower Mississippi River. He was assigned to the expedition by royal orders, probably issued on advice of the naval minister, the Marquis de Seignelay, as cartographer and engineer. During the voyage Minet kept a day-to-day journal and prepared several maps, including two of the Texas coast, which he took back to France to show La Salle's position. Copies of the Texas maps were acquired in 1686 by the Spanish ambassador in England, Pedro de Ronquillo, and forwarded to the viceroy in Mexico to aid the Spaniards' search for La Salle's colony.
La Salle regarded Minet with suspicion almost from the start. At Petit Goâve (Haiti) he removed his command post from the naval vessel Joly to continue the voyage on the storeship Aimable. Minet remained on the first ship and thus became identified in La Salle's mind with the naval commander, Tanguy le Gallois de Beaujeu, with whom La Salle was perpetually at odds. After the misplaced landing in Texas at Matagorda Bay, Minet's relationship with La Salle worsened further. When the Joly left La Salle and sailed for France in March 1685, La Salle ordered Minet aboard her with other rejects and defectors.
On arriving at Rochefort on July 6, 1685, Minet sent an "extract" of his journal and copies of his maps to Seignelay, with a cover letter; the package including his report of the voyage and of La Salle's desperate plight, as well as his own alibi for having deserted the enterprise. When the king heard the news, he promptly ordered Minet and Captain Aigron of the storeship Aimable, lost in the mouth of Matagorda Bay, imprisoned in St. Nicholas Tower at La Rochelle. Minet remained there forty days, during which time he completed his journal and appended a list of accusatory questions as an indictment of La Salle. Minet was freed on September 7 and assigned to work under the Marquis de Vauban, French commissioner of fortifications, but nothing more is known of his career.
His journal of the voyage to and from the Texas coast aboard the Joly became available to researchers in 1981, when it was acquired from private hands by the Public Archives of Canada in Ottawa. In addition to the journal, Minet composed during the voyage an account of La Salle's 1682 descent of the Mississippi River, from information given him by two participants, Nicolas de La Salle and the Sieur de Barbier. The narrative is joined to the journal in the Canadian archives' acquisition. Minet also drew a map of North America reflecting La Salle's confused geographical concepts.