Как вы отправляете данные для обработки php. я добавил скрипт к действию формы и заменил кнопку отправки на ввод типа submit
HTML
<form id="contact-form" action="my_processing_script.php">
<div class="form-field-item">
<input type="text" required="required" name="fullname" id="fullname" size="25" placeholder="Name" class="form-field">
</div>
<div class="form-field-item">
<input type="tel" id="phone" name="phone" required="required" placeholder="Contact Number" class="form-field">
</div>
<div class="form-field-item">
<input type="email" required="required" name="email" id="email" placeholder="Email" class="form-field">
</div>
<div class="form-field-checkbox-item">
<div class="checkbox-item">
<input type="checkbox" id="agree-gdrp" name="agree-gdrp" required="required" value="Yes">
<label for="agree-gdrp" class="field-label">I agree that Fraser handles my personal data in accordance with GDPR</label>
</div>
</div>
<div class="form-submit-wrap">
<input type='submit' value='Send Enquiry'>
</div>
</form>
my_processing_script. php
<?php
$recepient = "info@mail1.com,awhite@mail1.com";
$sitename = "Fraser";
$fullname = trim($_POST["fullname"]);
$email = trim($_POST["email"]);
$phone = trim($_POST["phone"]);
$message = "Name: $fullname \nContact Number: $phone \nEmail: $email";
$pagetitle = "Fraser Contact Form";
mail($recepient, $pagetitle, $message, "Content-type: text/plain; charset=\"utf-8\"\n From: info@mail.com");
?>
Если вы не хотите покидать страницу, я бы предложил опубликовать форму через ajax или jquery post
<button id="my-submit-button">Send Enquiry</button>
JQuery
$("#my-submit-button").click(function(e){
var fullname = $("#fullname ").val()
var phone = $("#phone ").val()
var email = $("#email ").val()
var agree_gdrp = $("#agree-gdrp").val()
$.post("my_php_sctipt.php", {"fullname" :fullname, "phone":phone, "email" : email , "agree_gdrp": agree_gdrp }).done(function(evt){
alert("data sent");
})
})