A faulty fuel pump won't cause a misfire directly but it can be part of the cause.
If the engine doesn't get enough fuel when the engine produces the spark to burn that fuel then a misfire can happen.
Most times when an engine is misfiring it's due to incorrect timing, bad spark plugs, bad ignition coil, or any other part of the ignition system.
You can take your car to Autozone and they'll usually be able to tell what is causing the misfire by bringing up the code on their code reader for you for free.