症状

Non-Ascii characters, like é, â, è are not being displayed correctly in the repository commit history, column Author. These characters are not displayed correctly only in the Author field. Usage of the same character in the commit message displays correctly.

Bitbucket Server and browser are both set to use UTF-8 encoding.

原因

This behaviour is related to Git itself. Bitbucket Server uses the same String encodings, in the server code, where it's loading the commit message as where it's loading the author name, indicating this is related to how Git is interpreting those characters, since they are correctly displayed in one place and not in another.

さらなるトラブルシューティング

For further investigation, it would help to have one of the users whose name shows up wrong in the author column make a commit to a test/demo repository and check if the problem can be replicated?

ソリューション 

Check how this Git repository was created? Was it migrated from another SCM - svn for example? The problem lies with how this migration came about and what tool was used.