Is Libre Office able to auromatically recognise the language I write and correct the spelling?
LibreOffice does not recognize language of writing automatically. It can use language information passed from operating system, though; it currently only works on Windows, and only when you have set up your input languages in operating system correctly, and switch these system input language when changing language of writing (rarely done by Roman-script language users, so I’d guess that you might not even knew your OS has such a feature).
(Sorry for the English answer on this French leg of the Ask site; just answering using the same language as the question itself.)
Thank you for answering.