Franson went undrafted in the 2002 WHL Bantam Draft. Nevertheless, the Vancouver Giants in the Western Hockey League offered him a tryout and Franson was successful in making the team. He played full-time for the Giants starting in the 2004–05 season, where he put up 13 points. Franson then improved to 55- and 51-point campaigns with the Giants in the next two seasons, respectively. In 2006, he helped lead the Giants to the President's Cup as WHL champions, earning a berth in the 2006 Memorial Cup. He then recorded the only hat-trick of the tournament and led all defencemen in scoring, with five points in five games. In the subsequent off-season, Franson signed an entry-level contract with the Predators in July 2006, the organization that drafted him in the third round, 79th overall, in 2005. The next year, he was named to the WHL West First All-Star Team and was nominated for the Bill Hunter Memorial Trophy as the League's top defenceman, although the Trophy was ultimately awarded to Kris Russell of the Medicine Hat Tigers. After falling to Medicine Hat in the 2007 WHL Final, Franson and the Giants captured the 2007 Memorial Cup as tournament hosts, defeating the Tigers in the final.
On July 3, 2011, Franson, along with forward Matthew Lombardi, was traded to the Toronto Maple Leafs in exchange for Brett Lebda and Robert Slaney. During the subsequent 2011–12 season, Franson played 57 games for the Maple Leafs, scoring 21 points and finishing with a plus-minus rating of –1. On October 1, 2012, Franson signed a contract with Brynäs IF of the Swedish Elitserien due to the 2012–13 NHL lockout. On January 13, 2013, he signed a one-year contract with Toronto as a restricted free agent. On May 13, Franson scored two goals for the Maple Leafs in Game 7 of the Eastern Conference Quarter-finals of the Stanley Cup playoffs against the Boston Bruins, a game Toronto eventually lost 5–4 in overtime. On July 21, 2014, Franson and the Maple Leafs agreed to a one-year contract extension worth $3.3 million.
Return to Nashville
Franson suited up for 55 games for the Maple Leafs during the 2014–15 season, recording six goals and 32 points. On February 15, 2015, Franson was traded back to the Predators, along with Mike Santorelli, in exchange for Olli Jokinen, Brendan Leipsic and a first-round draft pick. This marked both Santorelli's and Franson's second tenure with Nashville. Franson skated in 23 games with the Predators to close out the season. He also appeared in five postseason games, recording two assists.
Buffalo Sabres
Despite being ranked as one of the top free agents available during the offseason, Franson did not sign a contract until September 10, 2015 when he inked a two-year deal with the Buffalo Sabres worth $6.6 million total. Over his two seasons with the Sabres, entrenched in a top four role, Franson appeared in 127 games for 36 points but was unable to help the rebuilding club make the post-season.
Chicago Blackhawks
On September 7, 2017, Franson agreed to attend the Chicago Blackhawks' training camp on a professional tryout agreement. On October 4, the Blackhawks signed Franson to a one-year, $1 million contract. Franson spent the majority of the season with the Rockford IceHogs.
Avangard Omsk
On September 5, 2018, Franson signed his first overseas contract, joining Avangard Omsk of the KHL.
