Coach Steve Hansen also kept faith in struggling back Ben Smith but could find no room for rampaging midfielder Ngani Laumape as the New Zealanders target a third straight World Cup title and fourth overall.
Williams is among a trio of players hoping to secure an unprecedented treble in Japan, alongside captain Kieran Read and lock Sam Whitelock.
Another nine members of the squad tasted success at the last rugby showpiece in Britain four years ago, while 19 are World Cup debutants.
The squad collectively boasts 1,195 Test caps, including 121 for the indefatigable Read.
Hansen said winning three titles in a row was "an awesome challenge".
"We know it's going to be hard, we know it's going to be tough... we're looking forward to taking that pressure head-on," he said.
Williams, the oldest member of the squad at 34, shook off an injury-plagued season with a convincing performance in this month's 36-0 victory over the Wallabies in Auckland.
There was no such reprieve for Franks, whose 108-Test career comes to an end as Hansen seeks more mobility and forward momentum from his props.
Anton Lienert-Brown, Jack Goodhue and fellow veteran Ryan Crotty join Williams in the centres, with powerhouse ball-runner Laumape unlucky to miss out.
As expected, Hansen is persisting with his new tactic of using two playmakers -- Richie Mo'unga at fly-half and Beauden Barrett at fullback -- to counter opponents' rush defence.
An excellent Super Rugby season sees Brad Weber join TJ Perenara and Aaron Smith in the three halfbacks selected by Hansen.
Rieko Ioane, Sevu Reece and George Bridge ensure the defending champions have potency on both wings, along with the versatile Jordie Barrett.
Ben Smith also remains in the mix, although recent form struggles and Hansen's tactical switch makes him more likely to feature on the wing than at fullback.
Joe Moody, Ofa Tuungafasi, Nepo Laulala, Atu Moli and Angus Ta'avo form the front row, with Karl Tu'inukuafe joining Franks on the scrapheap.
Hookers Dane Coles, Codie Taylor and Liam Coltman were always regarded as certainties, with Coles probably edging Taylor as preferred starter.
Brodie Retallick returns from a shoulder injury to partner Whitelock in the locks, backed up by Patrick Tuipulotu and Scott Barrett, who can also play in the back row.
Read, Ardie Savea, Matt Todd and Luke Jacobson make up the rest of the loose forwards.
Dane Coles, Liam Coltman, Codie Taylor, Nepo Laulala, Joe Moody, Atu Moli, Angus Ta'avao, Ofa Tuungafasi, Scott Barrett, Brodie Retallick, Patrick Tuipulotu, Sam Whitelock, Sam Cane, Luke Jacobson, Kieran Read (captain), Ardie Savea, Matt Todd.
TJ Perenara, Aaron Smith, Brad Weber, Beauden Barrett, Richie Mo'unga, Ryan Crotty, Jack Goodhue, Anton Lienert-Brown, Sonny Bill Williams, Jordie Barrett, George Bridge, Rieko Ioane, Sevu Reece, Ben Smith.