If I paid my fine before my court date will the arrest show up on background check

The arrest will show up, not appearing in court, does not change it, paying the fine, is agree to plead guilty and agree to the fine.

With that said, this must be something very minor, perhaps a city violation ? Most times in criminal cases you can't just pay a fine but have to appear.

Paying the fine means you pleaded guilty, which means it shows up as a conviction. But, as Chuck said, if its something you can deal with by just paying the fine its very minor.