You will need to perform the following actions:

1. If you have Joom!Fish installed but you use it for everything else except items (articles), meaning you have created the multi-language content of your site by creating items per language inside the FLEXIcontent items manager then:
   -- disable the plugins:
   Search - Content  (standard Joomla article search plugin)
   Search - Jfcontent (Joom!Fish article search translate plugin)
   -- and enable the FLEXIcontent standard search plugin, and inside it activate language filter
2. If you have a single language inside the FLEXIcontent items manager and you use joomfish to translate article (items) then do the opposite of the above.

NOTE 1: Searching works only for title and description, but v1.5.6, there is a new search view, that allows searching more fields, and displaying more fields that just title and description. NOTE 2: to display custom FLEXIcontent fields in the joomla search component (com_search) results please read this forum thread