Is there a fee to enter the park for fishing?

Yes the standard $5 entrance fee applies.

Its a $5 fee per car to enter. There's no charge for fishing. You'd also want to check their rules if its catch and release only or if you can keep what you catch.

Day visit entry fee is $5 and night lights visit is $15, they do not charge for fishing

I'm not really sure. I just visit the lights in December.