The sticker on the swing arm of my '08 FZ6 says Fuel: All Gasoline 91 RON MIN. RON is an octane measuring standard used outside of the US. In the US, we use the CLC rating. According to the internet, 91 RON == 87 CLC. So you can interpret the sticker as saying 87 CLC MIN.
Octane is a combustion inhibitor that is there to prevent the fuel/air mixture from igniting prematurely as it is compressed in the cylinder before the spark plug fires. Your spark plugs will have no problem lighting off the mixture, be it 87 or 94 octane.
So yeah, the engine should run great on regular gas, and it should run the same on premium. Personally, I run premium because compression ratios in the neighborhood of what the FZ6's engine has have traditionally required higher octane fuel. Obviously, Yamaha has engineered it to run on 87, but I still pump it because it just makes sense to me. Maybe I'll learn something new down the road to change my mind, who knows...