FMS can use many inputs. INS is still part of the mix -- in the big airplanes, at least. The newer ones are actually IRUs, using lazer ring gyro's, and provide inputs in lateral and vertical path. The VSI and Attitude indicator, as well as the compass indication, all come off IRU inputs. It also inputs into the FMS, with only GPS being given a higher priority, depending on the RAIM (which the system tracks), as well as the ANP/RNP. The compass variation is adjusted thru a database rather than flux valves. I can also get the IRS altitude indication out of our CFDS, although that is not typically displayed on the panel.
The IRS portion of the FMS is a very important part of the redundancy that you want. GPS coverage isn't perfect all over the world, and it's nice to be able to navigate accurately with just internal systems.