Your code seems ok. With your code. If you want to test if your form is ok you can add a form action to redirect user after the right submit of your form like this (with action = "newPage.html):
<body>
<form id="loginForm" action="newPage.html">
Your mail:
<input type="email" name="email" id="email" required/>
<input type="submit" value="Save form" />
</form>
So now to test, you have to create the "newPage.html" file with the body you want:
<body>
<p>good submit</p>
</body>
If the new page appears, it's ok for your submit!