To change the language for the WebClient you can add a string to the URL, so you don’t need to change the language for the whole Browser:

https://client-ip-hostname:9443/vsphere-client/?locale=en_US

Mögliche Optionen wären:
English = /?locale=en_US
German = /?locale=de_DE
French = /?locale=fr_FR
Japanese = /?locale=ja_JP
Korean = /?locale=ko_KR
Chinese = /?locale=zh_CN