Just thought, if that would be possible, I can get users native language, and display my webpage on their language, or on the closest one. So;
Is it possible to get someone's language using his/her Google account cookies in somehow?
No, because you do not have access to Google's cookies. You only have access to the cookies your website sets.
To answer your question, you don't need to hack into Google's cookies to get that information, but can find it out yourself in your own code.
IMPORTANT NOTE: You are talking about automatically serving content to users based on their language settings, which can actually lead to a lot of SEO problems if done badly. A better option is to serve the URLs as normal, and if you detect that the user is viewing a different language version than their own, you provide a pop-up that offers to take them to the language of their choice. This approach will also allow you to correctly encode hreflang tags on your pages and will facilitate Google automatically picking up the most relevant language version to show users is search results.