The default Vuepress search plugin is aware that you're in a multilingual site, and searches only the current language. As this is now I get the same doc in all translations where there is any common text.

EDIT: Note, I could be incorrect here - the default-header only search may simply not show the translations because most headings are translated. Either way it is a flaw - as a user I am would probably only be interested in matching translations as a "last resort"