Up grading my Trek FX 3

[Seaker]

Will a Shimano 105 gear system and crank set fit a 2017 FX 3 with straight across handlebar

 

[si_c]

Yes it should do.

You will need the SL-RS700 shifters which are the flat bar ones and they will match up with the rest of the R7000 groupset fine. You'll keep your existing brakes and levers.

 

[Dogtrousers]

One thing to double check is your freehub. R7000 is 11 speed, so your freehub needs to be able to take an 11S cassette.

May be fine, may not be. May require a spacer - I'm not sure. Not saying it won't be fine, but it may be worth double checking.