Although Justice League: War adapted writer Geoff Johns and artist Jim Lee’s Justice League arc that opened the New 52 reboot, the movie decided to use Shazam as one of the founding Justice Leaguers rather than Aquaman (Arthur Curry debuted a year later in Justice League: Throne of Atlantis).
Arguably the biggest difference between Shazam’s costume in the movie and the traditional Captain Marvel costume is the hood, which was a carryover over from Shazam’s New 52 reintroduction (which was also written by Johns).
Voiced by Sean Astin, Shazam joined Batman, Superman, Wonder Woman, Flash and Green Lantern in repelling Darkseid’s invasion.
The Shazam! movie is incorporating several notable elements from Shazam’s New 52 stories, like Billy Batson living with a foster family and the look of the Wizard who gives him his powers, so it’s not terribly surprising to learn that Shazam’s cinematic costume is partly inspired by that era.