Unzip_file is not working

I’m creating a plugin right now that tries to download a zip file and then extract it to my plugin directory. I can download it just fine, but I can’t extract it using the unzip_file function.

Here is my code:

$path =  plugin_dir_path(__FILE__);
$remote_file = 'file.zip';
$local_file = $path . 'file.zip';

$ftpstream = ftp_connect('ftpname');
$login_result = ftp_login($ftpstream, 'ftp-username', 'ftp-password');
ftp_get($ftpstream, $local_file, $remote_file, FTP_BINARY);
ftp_close($ftpstream);

The part above works perfecly fine, the file gets downloaded, but here is the problem:

chmod( $local_file, 0777 );
WP_filesystem();
unzip_file( $local_file, $path );

I checked and everything (downloading, giving file permission) works. It just doesn’t seem to extract and also never return any error.
I think the problem comes from calling WP_filesystem incorrecly, but I can’t find how to make it work…

Thank you for your help!