Is there a way to change the order of the fields that show up on the Pro-Form?

If you're using Custom Registration Fields (see: WordPress Dashboard s2Member General Options Registration/Profile Fields & Options) you can customize the order of those fields in a Pro-Form by re-ordering them via drag n' drop.

However, the order of standard fields, such as First Name, Last Name, Email Address, etc., cannot be customized at this time. It's also not possible to move Custom Registration Fields outside of the Custom Fields section of the Pro-Form. That is, not unless you build a custom Pro-Form template of your own. See: Customizing Pro-Forms for more information about this topic.