Forza Horizon 3 was never released on Xbox 360.
It launched September 2016 exclusively on:
Why? The game's open world, graphics engine (ForzaTech), and online infrastructure required the Xbox One's unified 8GB DDR3/ESRAM architecture and x86 CPU. The Xbox 360's PowerPC architecture and 512 MB RAM were insufficient.
Xbox 360 Forza Titles: Forza Motorsport 2, 3, 4 and Forza Horizon 1 (2012) are the only Forza games on the platform.