Franklin finished with four goals and set up several others as the Hawks pulled steadily away in the first half, then buried the Blues with a six goals to one third term.
Jarryd Roughead (three goals) and Jack Gunston (three) shared in the spoils, as Hawthorn's star-studded attack made light work of the Blues' injury-hit defence.
Franklin took his season tally to 47, 12 clear of his nearest rival, Richmond's Jack Riewoldt.
It was the Hawks' fourth straight win, taking them to a 9-4 record and firmly in the hunt for a top four berth, with a very winnable clash with Greater Western Sydney to come next Sunday at the MCG.
For the Blues, it was their fourth straight defeat, and ninth in succession against the Hawks, leaving them on a 6-7 record and further adrift from the top eight.
Having started the season with three big wins to leap to premiership favouritism, they have now lost seven of their past 10 games and face top-placed Collingwood at the MCG next Friday night.
Missing defenders Lachie Henderson and Jeremy Laidler, they found it impossible to contain Hawthorn's tall forwards, particularly with the speed and precision with which the Hawks delivered the ball into attack.
Not helping their cause, fullback Michael Jamison left the field with a shoulder injury late in the third term and did not return.
Franklin kicked three goals in the first half to help his side to a 29-point lead.
While the Blues showed some fight early in the third quarter, it quickly faded, Hawthorn dominating the last 20 minutes of the term to kick five unanswered goals.
Hawks midfielder Brad Sewell had a strong game, extracting 10 clearances and 18 contested possessions while battling hard against Carlton skipper Chris Judd, with Sam Mitchell (32 disposals, one goal) also a driving force.
Judd also worked hard, for 29 touches and a goal, while Andrew Carrazzo also battled valiantly in the ground level contests.
The one sour note for the Hawks was a likely suspension to defender Brent Guerra for a first-term incident.
Guerra delivered a high front-on bump on Carlton's Eddie Betts, while the small forward was bent over the ball, with Betts goaling from the resultant free kick.
Franklin ended the game on the bench after feeling at his left hamstring.
Hawks coach Alastair Clarkson said Franklin experienced hamstring tightness but it was not believed to be a major injury.
"We'll get that scanned early in the week and see. I don't think it's too serious, whatever it is," Clarkson said.
"If there's a slight strain there he might miss a week, but he's such a resilient big fella it wouldn't surprise me one bit if he played next week."
Blues coach Brett Ratten said he did not know the extent of the damage to Jamison's shoulder.
"He'll have a scan tomorrow and we'll find out the results from there," Ratten said.
"He's had a history of shoulder (injuries) so I don't know what's going to happen there."