Drupal's default 'Generic File' format can be a bit ugly. Luckily, it's not too hard to override. If you'd like to change the default filefield theming for 'Generic File', try using the theme_filefield_item() function in your template.php file.
Note: You may also be interested in checking out my post on customizing the filefield format in views.
In the example below, I overrode the default theming for all cck fieldfields belonging to node type 'publication'.