Detroit has opened the season with a 5-0 record and has outscored the opposition 18-7. Washington is the only other team in the NHL without a loss this season.
Columbus remained the lone winless team in the league, falling to 0-6-1.
Franzen scored his third and fourth goals of the season 5:18 apart during the middle portion of the opening period.
Columbus twice closed within one goal, but could never get the game tied. Nicklas Lidstrom gave Detroit a 4-2 lead with another power-play goal 7:46 into the third period and Valtteri Filppula scored into an empty net with 1:27 remaining.
Jimmy Howard, who has been in goal for four of Detroit's five victories, made 29 saves.
Steve Mason stopped 28-of-32 shots in taking the loss.