Véronneau played junior ice hockey in his hometown of Ottawa, then joined the Princeton University Tigers.
After playing junior 'A' ice hockey in Ottawa, Ontario, with the Gloucester Rangers, Véronneau entered Princeton University in 2015.
[4] At the beginning of the 2019–20 season, Véronneau was assigned to Ottawa's American Hockey League (AHL) affiliate, the Belleville Senators.
[8] As a free agent from the Maple Leafs, and with the 2020–21 North American season delayed due to the pandemic, Véronneau opted to sign his first contract abroad in agreeing to a contract for the remainder of the season with Swedish club, IK Oskarshamn of the Swedish Hockey League (SHL), on December 21, 2020.
[9] In the top Swedish tier, Véronneau regained his offensive confidence, potting 12 goals through 25 regular season games with IK Oskarshamn.