In the 2020–21 season, Jeannot made his NHL debut appearing in a fourth-line role for the Predators in a 4–2 defeat against the Carolina Hurricanes on March 2, 2021.[4][5] Despite pacing all rookies in goals (24) and hits (318) in the 2021–22 season, Jeannot was not a finalist (top 3 in voting) for the Calder Memorial Trophy.[6]
In the 2022–23 season, Jeannot playing in the final season of his entry-level contract with the Predators, was unable to match his rookie season offensive pace in registering five goals and 14 points through 56 regular season games. With the Predators losing ground for playoff contention, Jeannot was traded by Nashville to the Tampa Bay Lightning in exchange for defenceman Cal Foote, along with a package of five draft picks, including a 2025 first-round pick (lottery protected) on February 26, 2023.[7]
On June 29, 2024, Jeannot was traded by the Lightning to the Los Angeles Kings for a fourth-round pick in the 2024 NHL entry draft and a second-round pick in the 2025 NHL entry draft.[8]