Contact form not found on localhost

I get the following error when I send a message from my contact form:

POST http://localhost:3000/mail/contact_me.php 404 (Not Found)

I'm not sure if it has to do with the structure of my files or trying to POST on localhost.

Things I checked:

1. The form has method="post".
2. The ajax request is type: POST
3. The inputs have name='something'
4. The page is running properly on localhost:3000

What do I need to fix?

Here is the structure of my app:

app.js:

const
    express = require('express'),
    app = express(),
    logger = require('morgan'),
    bodyParser = require('body-parser')

// environment port
const port = process.env.PORT || 3000

app.use(express.static(process.env.PWD + '/client'))
app.use(logger('dev'))
app.use(bodyParser.urlencoded({extended: true}))
app.use(bodyParser.json())

app.get('/', (req, res) => {
  res.render('index')
})

app.listen(port, (err) => {
  console.log(err || 'listening on port ' + port)
})

Here is the ajax request in client/js/contact_me.js:

        $.ajax({
            url: "../../mail/contact_me.php",
            type: "POST",
            data: {
                name: name,
                phone: phone,
                email: email,
                message: message
            },
            cache: false,
            success: function() {
                // Enable button & show success message
                $("#btnSubmit").attr("disabled", false);
                $('#success').html("<div class='alert alert-success'>");
                $('#success > .alert-success').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                    .append("</button>");
                $('#success > .alert-success')
                    .append("<strong>Your message has been sent. </strong>");
                $('#success > .alert-success')
                    .append('</div>');

                //clear all fields
                $('#contactForm').trigger("reset");
            },
            error: function() {
                // Fail message
                $('#success').html("<div class='alert alert-danger'>");
                $('#success > .alert-danger').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                    .append("</button>");
                $('#success > .alert-danger').append("<strong>Sorry " + firstName + ", it seems that my mail server is not responding. Please try again later!");
                $('#success > .alert-danger').append('</div>');
                //clear all fields
                // $('#contactForm').trigger("reset");
            },
        });

mail/contact_me.php:

<?php
// Check for empty fields
if(empty($_POST['name'])        ||
   empty($_POST['email'])       ||
   empty($_POST['phone'])       ||
   empty($_POST['message']) ||
   !filter_var($_POST['email'],FILTER_VALIDATE_EMAIL))
   {
    echo "No arguments Provided!";
    return false;
   }

$name = strip_tags(htmlspecialchars($_POST['name']));
$email_address = strip_tags(htmlspecialchars($_POST['email']));
$phone = strip_tags(htmlspecialchars($_POST['phone']));
$message = strip_tags(htmlspecialchars($_POST['message']));

// Create the email and send the message
$to = 'myemail@gmail.com'; 
$email_subject = "Website Contact Form:  $name";
$email_body = "You have received a new message from your website contact form.\n\n"."Here are the details:\n\nName: $name\n\nEmail: $email_address\n\nPhone: $phone\n\nMessage:\n$message";
$headers = "From: noreply@yourdomain.com\n";
$headers .= "Reply-To: $email_address";
mail($to,$email_subject,$email_body,$headers);
return true;
?>

Here is the form in client/index.html:

<form name="sentMessage" method="post" id="contactForm" novalidate>
    <div class="row control-group">
        <div class="form-group col-xs-12 floating-label-form-group controls">
            <label for="name">Name</label>
            <input name="name" type="text" class="form-control" placeholder="Name" id="name" required data-validation-required-message="Please enter your name.">
            <p class="help-block text-danger"></p>
        </div>
    </div>
    <div class="row control-group">
        <div class="form-group col-xs-12 floating-label-form-group controls">
            <label for="email">Email Address</label>
            <input name="email" type="email" class="form-control" placeholder="Email Address" id="email" required data-validation-required-message="Please enter your email address.">
            <p class="help-block text-danger"></p>
        </div>
    </div>
    <div class="row control-group">
        <div class="form-group col-xs-12 floating-label-form-group controls">
            <label for="phone">Phone Number</label>
            <input name="phone" type="tel" class="form-control" placeholder="Phone Number" id="phone" required data-validation-required-message="Please enter your phone number.">
            <p class="help-block text-danger"></p>
        </div>
    </div>
    <div class="row control-group">
        <div class="form-group col-xs-12 floating-label-form-group controls">
            <label for="message">Message</label>
            <textarea name="message" rows="5" class="form-control" placeholder="Message" id="message" required data-validation-required-message="Please enter a message."></textarea>
            <p class="help-block text-danger"></p>
        </div>
    </div>
    <br>
    <div id="success"></div>
    <div class="row">
        <div class="form-group col-xs-12">
            <button type="submit" class="btn btn-success btn-lg">Send</button>
        </div>
    </div>
</form>

via user2456977