Why Google Captcha not working in my new server, But In the old server, it was working fine and key and the secret key is the same for both servers. After doing all kinds of research I found the solution, that Some Module needs to install in my new server, for that reason file_get_contents($url) is not working, The module name is allow_url_fopen.
If you have WHM access then you can do by yourself. Just have a look below image then you can fix it by easily.
Step-1: Login Your WHM and search PHP
Step-2: GO and click MultiPHP INI Editor.
Step-3: Choose your PHP version.
Step-4: Enable allow_url_fopen module.
Step-5: Save Changes.
Now it works fine