A hardy crowd of 3,045 watched Franklin struggle on his Swans debut, but so did he majority of his teammates in steady drizzle and slippery conditions.
Well held by Mitchell Brown, Franklin tallied six touches, three marks and just one behind.
His solitary score was a 55-metre set shot which went just wide to the right.
West Coast followed up their 84-point rout of Fremantle with another encouraging performance, especially in the second half.
Between them, the teams kicked five goals in the first half, with Sydney leading by one point at the first break and by four at halftime.
The Eagles kicked 7.5 to 0.0 from late in the second quarter to early in the fourth to take control.
Callum Sinclair and Brant Colledge both kicked two goals for the visitors.
Sinclair, Brown Elliot Yeo, Xavier Ellis and Chris Masten were among the Eagles' best performers.
Gary Rohan kicked three goals for Sydney, while the Swans' Heath Grundy and Craig Bird led the possession-getters with 35 and 32 respectively.
After a well-contested first half, West Coast dominated out of the centre and kicked a series of goals from close range.
Franklin moved to centre half back in the third quarter, but collected just one touch for the term as the Eagles dominated.
A frustrated Franklin gave away a couple of free kicks in the second half as he tried hard to inject himself into the game, though the tide of action was flowing against the Swans.
Young Sydney midfielder Luke Parker had a bandage wrapped across his face and covering his right eye after coming off in the second quarter, while Rohan appeared to get an ankle knock, but came back on.
"To break open in the third quarter was pleasing, but it was the first half I was impressed with," Eagles coach Adam Simpson said.
"Just our ability to hunt the footy and our intent.
"We probably missed our senior spine, so our younger players filled the void really well."
Asked how Brown contained Franklin, he joked "trade secrets.'
Sydney coach John Longmire lamented his team'S inability to win the ball and deliver good quality service to Franklin and Sam Reid up forward.
"We just didn't win the ball, we were minus 40-odd for the game in contested ball and in that particular (third) quarter we were probably minus 16 or 17 in contested ball," Longmire said.
"It was pretty difficult for the forwards, when he (Franklin) and Reidy, when we are only getting 18 inside 50s in the first half."
Longmire said using Franklin further up the ground was not necessarily indicative of how he would be employed once the season starts and he just wanted to get some run into his legs.
"His running was fine and his pressuring and competing, he was fine that way. We just didn't get of the ball forward," Longmire said.
Simpson reported no injuries, while Longmire said Parker was getting his eye checked out at a hospital and wasn't sure of the extent of the issue.
WEST COAST 0.1.5 0.2.6 0.8.10 0.10.12 (72)
SYDNEY 0.2.0 0.3.4 0.3.4 0.5.7 (37)
Nine pointers: West Coast - Nil. Sydney - Nil.
Goals: West Coast - Colledge, Sinclair 2; Masten, McInnes, Cripps, Darling, Selwood, Wellingham. Sydney - Rohan 3; Towers, Reid.
Best: West Coast - Sinclair, Brown, Yeo, Masten, Ellis, Rosa. Sydney - O'Keefe, Rohan, Shaw, Malceski, Grundy.
Umpires: Robert Findlay, Jacob Mollison, Brent Pawley.
Venue: Blacktown Olympic Park.