Once a file entity is configured, its display can be managed.
It is possible to activate custom display settings for many view modes: full content, teaser, preview...

So far, great!

Only the display settings for "Search result" won't work.
They have no impact whatsoever on the display of the search results: these literally follow search-result.tpl.php.

I can make a website with entities (say images). I can add fields to them (captions, a description...). These images are searchable as entities.
To make the search results logical: is there a way to re-write "search-result.tpl.php" to show the rendered images on this page, instead of their file names?

P.S. Display suite can overrule the search results page, but it's not compatible with File Entities. So that's no option...