The following affects Confluence and JIRA alike:
If I enter an umlaut character in Quick Search, like "ä" I get "ä" in the resulting search result page (Confluence). In Jira I get an "ü".
I also get zero hits (both in Confluence and in JIRA)
Eg. in Confluence we go a user called "Martin Küpperbusch". I don't get a hit when I search for "küpperbusch" - but I get one when searching für "K?pperbusch". Same effect in JIRA.

So search of non-ascii characters seems to be messed up.