Display user's email address and name in a form

if you hover over people picker entry it shows a popup with user details.

would that be sufficient for you?

I need the user's email in one of the fields but I would like to retrieve that information from sharepoint

then you can use sharepoint's REST API to get the info.

users should be accessible under http://<site url>/_api/web/siteusers endpoint

if you are on nintex enterprise you can use web request control to get data from that service, if not you will need to write your own javascript handler.