You should start with looking at the URL class. http://docs.groovy-lang.org/latest/html/groovy-jdk/java/net/URL.html
That will allow you to read the whole page under a certain URL using getText(). If the page is down, this will throw an exception.
Jenkins should then automatically fail the job. In the Jenkins job definition, you can specify when and how to send a Mail.
EDIT This isn't valid Groovy: (curl -Is https://google.com | head -1). Groovy can't run shell commands or build pipes with | like BASH does. Also, you have to use {} around the then/else blocks after the if, not (). Lastly, there is no fi in Groovy:
if (condition) {
...then...
} else {
...
}
See Groovy executing shell commands for how to run shell commands from Groovy scripts.
Not that you have to examine the result of exitValue() to determine whether the command failed. 0 is success.