Jackson Houck, Kale Kessy, Riley Kieser, Brett Kulak and Carter Popoff also scored for the struggling Giants (8-20-0).
Steven Hodges and Logan Nelson tallied for the Royals (15-14-0).
Vancouver opened the scoring late in the first period when a spin-around shot by Franson went off a Royals defender and past goaltender Patrik Polivka.
The Giants made it 2-0 with just eight seconds left in the first when Houck blasted in a low point shot on the power play.
The Giants stretched their lead to three goals early in the second period as Kessy deflected a quick shot by Wes Vannieuwenhuizen, chasing Polivka from the Royals net.
The Royals got on the board with just over seven minutes left in the middle frame, making it 3-1 when a Giants defenceman deflected the puck into his own net after Hodges took a weak shot.
Vancouver responded quickly though, regaining the three-goal lead when a low snapshot by Kieser beat relief goalie Coleman Vollrath. Victoria made it 4-2 when Nelson batted in a loose puck in the crease.
Vancouver took a commanding 5-2 lead early in the third period when Kulak poked a loose puck under Vollrath.
Less than a minute later Franson potted a rebound for his second of the game, and then Popoff backhanded one in from the slot to finish the game at 7-2.
Giants goalie Payton Lee made 31 saves in the win.
Polivka stopped 12 of 15 shots before being pulled. Vollrath stopped nine of 13 shots.