As a youth, Bigras played in the 2008 Quebec International Pee-Wee Hockey Tournament with the Barrie Coltsminor ice hockey team. He later played junior ice hockey with the Owen Sound Attack in the Ontario Hockey League. During the 2012–13 season he played with Team Canada to win gold medals at both the 2012 Ivan Hlinka Memorial Tournament and the 2013 IIHF World U18 Championships. He was rated as a top prospect eligible for the 2013 NHL Entry Draft before he was selected by the Avalanche. During his first training camp with the Avalanche, Bigras impressed immediately from the blueline and was signed to a three-year entry level contract with the Avalanche on September 17, 2013. His performance was praised by head coach Patrick Roy and as a result, he was amongst the final cuts in being returned to the Attack of the OHL for the 2013–14 season. Bigras was named as an Alternate captain and although failing to reproduce his previous season offensive numbers with a weaker Owen Sound squad, he was voted by the league's coaches as the OHL best defensive defenseman. Over the summer, Bigras attended Canada's National junior development camp before participating in his second training camp with the Avalanche. Bigras failed to replicate his form from his initial camp and was reassigned to Owen Sound at the conclusion of camp. In his last season of junior in 2014–15, Bigras was relied upon as the Attack's number one defenseman. He continued his development to break out offensively in leading all blueline teammates in each scoring category with 20 goals, 51 assists and 71 points in 62 games, finishing second in the OHL. He earnt selection to the OHL First All-Star team and surpassed Owen Sound All-time scoring records in leading the club amongst defenseman with 120 assists and 155 points in his junior career.
Professional
After a first round defeat in the post-season signalling the conclusion of his OHL career, Bigras was signed to an amateur try-out contract with the Avalanche's AHL affiliate, the Lake Erie Monsters on April 7, 2015 and made his debut that night against the Chicago Wolves. Bigras recorded his first professional point, an assist, in the following game against the Rochester Americans on April 9. With the Monsters out of playoff contention, he finished the campaign with 4 assists in 7 games. Bigras was assigned to begin his first full professional season in 2015–16 season, with new Avalanche AHL affiliate, the San Antonio Rampage. He established himself amongst top-pairing minutes with the Rampage, appearing in every contest and placing second amongst the defense in scoring before he received his first NHL recall to the Avalanche on January 13, 2016. Bigras made his NHL debut with the Avalanche in a 3-0 victory over the New Jersey Devils on January 14, 2016. He collected his first NHL point on an assist in the following game against the Columbus Blue Jackets on January 16. Bigras was initially placed on the third pairing to continue his development, showing his defensive prowess, before scoring his first NHL goal in his 21st game in a 6-3 defeat to the Minnesota Wild on February 2, 2016. In the 2017–18 season, Bigras made the Avalanche opening night roster out of training camp. He appeared in 15 games with the Avalanche, registering a lone assist before he was reassigned to the San Antonio Rampage on November 28, 2017. Bigras suffered an injury with the Rampage and was limited to 20 games before he was dealt by the Avalanche at the NHL trade deadline to the New York Rangers in exchange for Ryan Graves on February 26, 2018. Following the conclusion of his contract with the Rangers, Bigras was not tendered a qualifying offer and was released as a free agent on June 25, 2019. Bigras was signed to a two-year, two-way contract with the Philadelphia Flyers on July 1, 2019.
