I have my language files in /language/ en.php, se.php etc

Here a snippet from one file:

$lang = array (

    'IMAGE_NOT_FOUND' => 'Kunde ej hitta bilden.',
    'ACCOUNT_ALREADY_ACTIVATED' => 'Ditt konto har redan aktiverats.'
    ...

);

Current code

if (isset($_GET['setlang']) && $_GET['setlang'] == 'en') include('language/en.php');
elseif (isset($_GET['setlang']) && $_GET['setlang'] == 'se') include('language/se.php');

How would I do to save lang for next visit even if user closes browser?

You would could a cookie if the user does not have to login, otherwise you could save it in the database.

Take a look at sessions for saving data across browser requests.