You have to redirect them to the right uri and not the homepage. E.G. : you are on /company/product, you change of language, you go to the homepage.
In eZPublish, multisites with different languages are specifies by their different siteccesses, one by language. So you just have to concat your language siteaccess with the know url of the current page.
So, you must edit the flag template and edit the links to have this.
