Wordpress - Why when I submit a form in wordpress it loads a 404 page though URL is correct

I could be wrong, but I vaguely remember that: name, email get hijacked by WordPress to do post comments, if you renamed the form elements to be contact-name and contact-email, do you get the same issue?

It is no only name or email problem, as Tom wrote. I had problem even with input field with name attribute same as one of my Custom Post Types. For example:

...
<input type="text" name="movie">
...

And when having registered CPT "movie" somewhere else, your form submitting will end with 404 error.

Conclusion: Don't use name, email and any registered custom post type handle as input name attribute value in your forms.

Try to change name="email" to something like name="my_theme_email", do the same with all your field it sounds like some name are reserved with WordPress when sending form data. I got the the same problem and I fixed it like that.