Field output is generated internally and is hardcoded internally. There's no templating available for fields HTML itself. You'd only be able to make some adjustments to the surrounding HTML in your template file found below, but unless you make your own template plugin you will lose your changes after each update.
/components/com_comprofiler/plugin/templates/default/default.php
Typically for profile display you can accomplish whatever field layout you like using substitutions in a Custom HTML field. For profile edit it's typically best to try and use CSS as there isn't really any options available beyond that for profile edit.