Truth be known, the frizzen springs only function is to keep the frizzen/pan cover closed over the pan and keep the frizzen from bouncing back and whacking the top jaw or flint after the flint has knocked it forward.
With the spring removed, if the pan is primed and the frizzen/pan cover is moved to the upright position, the flint should make sparks and the prime in the pan should fire.
Of course, it is nice to have a frizzen that keeps the pan cover closed and whacking the top of the top jaw or flint isn't the best thing to have happen.
If the frizzen moves freely when the spring is removed, I suggest reducing the width of the spring by filing or grinding it down to about 1/2 of its width. Leave the full width up in the area where the cam on the frizzen presses against it.
This may or may not fix the problem with the flint not fully opening the pan.
If the mainspring is weak or if the frizzen is too soft so the flint just digs into it rather than shearing off thin slivers of spark making metal, the problem may still be there.
Before frinkling with the spring width, remove the spring entirely and try the gun with the cock fully cocked and the frizzen closed.
If it does make sparks and knocks the frizzen forward rather than hanging up, then consider changing the spring.