Franzen's hat trick was his first since November 2011.
The Red Wings also got goals from Tomas Tatar, Riley Sheahan and Tomas Jurco in winning a second straight since returning from the Olympic break.
Niklas Kronwall distributed three assists.
Jonas Gustavsson got the victory with 37 saves.
Bobby Ryan notched only the only goal for the Senators, who fell to 2-3-1 in February.
Robin Lehner started in net but was yanked after yielding six goals on 15 shots.
Rookie Andrew Hammond relieved and stopped 11-of-11 shots in his NHL debut.