Is it possible to play with Xbox One players when playing the 360 Version?
As of right now, this isn't possible and it's likely it never will be. It seems a lot of news articles speculate the possibility of it coming to FIFA 17, but that's between Xbox One and PC (through Microsoft's new Cross Play ability) and not between Xbox 360 and Xbox One.
There are few exceptions where cross platform play is possible between Xbox One and Xbox 360. This answer explains the only times its possible. But to clarify as one user commented in the answer, when you play a backwards compatible Xbox 360 title on an Xbox One, you are actually running an Xbox 360 emulator that connects to the servers for Xbox 360s. But, since FIFA 17 isn't on the backwards compatibility list and since it is also made for Xbox One, you won't see it added to the list.