PHP read and write JSON from file
The clue is in the error message - if you look at the documentation for json_decode note that it can take a second param, which controls whether it returns an array or an object - it defaults to object.
So change your call to
$json = json_decode(file_get_contents($file), true);
And it'll return an associative array and your code should work fine.
The sample for reading and writing JSON in PHP:
$json = json_decode(file_get_contents($file),TRUE);
$json[$user] = array("first" => $first, "last" => $last);
file_put_contents($file, json_encode($json));