I am not sure if it can be done from the $image variable, but to get the MimeType, you can usually use any of the four:
// with GD
$img = getimagesize($path);
return $img['mime'];
// with FileInfo
$fi = new finfo(FILEINFO_MIME);
return $fi->file($path);
// with Exif (returns image constant value)
return exif_imagetype($path)
// deprecated
return mime_content_type($path);
From your question description I take you want to use a remote file, so you could do something like this to make this work:
$tmpfname = tempnam("/tmp", "IMG_"); // use any path writable for you
$imageCopy = file_get_contents('http://www.example.com/image.png');
file_put_contents($tmpfname, $imageCopy);
$mimetype = // call any of the above functions on $tmpfname;
unlink($tmpfname);
Note: if the MimeType function you will use supports remote files, use it directly, instead of creating a copy of the file first
If you need the MimeType just to determine which imagecreatefrom
function to use, why not load the file as a string first and then let GD decide, e.g.
// returns GD image resource of false
$imageString = file_get_contents('http://www.example.com/image.png');
if($imageString !== FALSE) {
$image = imagecreatefromstring($imageString);
}