If you're not busy this weekend, would you like to go fishing together?
Literal
Busy-if-not this-weekend [at-に] together fish-catching [to-に] go-won't-you?
忙しくなければ is the negative ~ば conditional of an i-adjective. 魚釣りに行く uses に to mark purpose/destination. ~ませんか is a polite invitation form — literally 'won't you [go]?' — softer than ~ましょう which presumes agreement. Combines conditional + invitation naturally.