We would like to have the search function to support special characters. See example below.

This can be achieved by the using the suggestion of Anoop:

We use Apache Lucene internally to do search. Our implementation uses StandardAnalyzer and KeywordAnalyzer from Lucene. In order to achieve what you are asking for we need to incorporate ASCIIFoldingFilter into our Analyzer. As of now this is not available as configuration or something that could be plugged in by you. Please raise an enhancement through support. We have in our roadmap to enhance our Search capabilities and this enhancement is a very important one for non-English Languages (especially European ones).

Link to forum post:  https://community.progress.com/community_groups/rollbase/f/25/t/20354

Example: 

We are searching (in the right top search box) for example a user: "Véronique"

Result is the user is found. To find it we have to enter the name with é in it. When we use "Veronique", the user is not returned to the search results.