First of all, make sure you have a graphics card that supports freesync. NVIDIA recently released a driver update which makes it possible to use G-sync on some "G-sync compatible" freesync monitors, so if you have an NVIDIA card, it's worth checking if G-sync works on your monitor. If you have an AMD card you can only use freesync.
Second of all, make sure freesync is enabled in your monitors settings.
Third, make sure freesync/g-sync is enabled in AMD/NVIDIA control panel.
And lastly, cap your fps at a few frames below your monitors refresh rate, as freesync/g-sync will not work if the refresh rate maxes out.
Your fps dropping to 65fps shouldn't impact freesync/g-sync, since the lowest variable refresh rate is usually lower than that. Though it might not be for your specific monitor.
To achieve a more stable fps you could either lower graphics settings to reach your framecap, or lower your framecap to reflect your fps.
Having a stable fps shouldn't really matter with freesync/g-sync though, as stuttering should be eliminated by the variable refresh rate.
Also, it's always a good idea to seek out as many sources as possible to cross-reference from, so make sure to do that as I might be completely wrong.
The thing is with FPS is that when you introduce a limiter of FPS. It will introduce input lag as well. There are the benefits are less screen tearing. But just like spooky salad said. The ability to have Gsync or adaptive sync and sync the amount of frames that are being displayed with the metal frames being out put it by the graphics card will eliminate both of those issues