On May 3, 2013, the Lightning signed Paquette to a three-year, entry-level professional contract,[2] assigning him to their American Hockey League (AHL) affiliate, the Syracuse Crunch, to start the 2013–14 season.

[7] On April 27, he scored his first career Stanley Cup playoff goal in a 5–2 Lightning win over the Red Wings in the Eastern Conference Quarter-finals.

[10] During the 2018–19 season, Paquette had a career-high 13 goals along with 4 assists and 17 points in a career high 80 games with the Lightning and led the team in penalty minutes.

[12] On December 27, 2020, Paquette's seven-season tenure with the Lightning ended as he was traded along with Braydon Coburn and a second round pick in 2022 to the Ottawa Senators in exchange for Marián Gáborík and Anders Nilsson.

[14] On February 13, 2021, after a very brief stint with the Senators, Paquette, who played in nine games, was traded along with Alex Galchenyuk to the Carolina Hurricanes in exchange for Ryan Dzingel.

[16] As a free agent from the Hurricanes, Paquette joined his fourth club in short succession by agreeing to a one-year, $950,000 contract with the Montreal Canadiens on July 28, 2021.

[17] As a free agent from the Canadiens, Paquette went overseas and accepted a contract with Belarusian club, HC Dinamo Minsk of the KHL, on August 16, 2022.

[18] Following a successful lone season with Minsk, Paquette extended his career in the KHL by signing a two-year contract with Russian based club, HC Dynamo Moscow, on May 2, 2023.