You will know it’s active when it shows seconds in the timer. You will see the last 4-5 seconds of the active skill being timed. Also the coolown lasts twice as much as the active skill.
Go into a pack of monsters, let yourself hit and right after you see fighting spirit proc go check your damage.
Btw. Fighting spirit> than Arcane will in my opinion. Arcan will is just fine at 1 point and let + skills do the rest