How to submit a form

Hi, I’m am a developper and I wonder how to submit my form. I’ve created it in my function.php file that is linked to my template page with a shortcode. The form works, I can fill it, but I can’t verify if it works, I don’t know why. I’m new to wordpress AND ajax and I don’t understand how wordpress manages it. Also, in my template, I have created two script tags (one for the phone number input and the second one to verify the form: the one I think it doesn’t work)). So, my form is visible, fillable, but I try to verify the submission and to save my data in a data table I have also created. Here is what I have done:

functions.php:

function registration_form() {
        ob_start();?>
        <form action="" id="registration_form" method="post">
                <input class="gauche" name="nom" type="text" placeholder="Nom*" required><input class="droite" name="prenom" type="text" placeholder="Prénom*" required>
                <input name="mail" type="email" placeholder="E-mail" required>
                <input name="login" type="text" placeholder="Identifiant*" required>
                <input class="gauche" name="mdp" type="password" placeholder="Mot de passe*" required><input class="droite" name="mdp2" type="password" placeholder="Confirmez le mot de passe*" required>
                <input name="societe" type="text" placeholder="Société*" required>
                <input name="fonction" type="text" placeholder="Fonction*" required>
                <input name="adresse" type="text" placeholder="Adresse*" required>
                <input name="complement" type="text" placeholder="Complément d'adresse">
                <input name="ville" type="text" placeholder="Ville*" required>
                <label id="pays">Pays <span style="color: red;">*</span></label>
                <input class="gauche" name="code" type="text" placeholder="Code postal*"><select class="droite" name="pays" required>
                        <option value="Afghanistan">Afghanistan</option>
                        <option value="Åland Islands">Åland Islands</option>
                        <option value="Albania">Albania</option>
                       </select>
                <label>Téléphone <span style="color: red;">*</span></label><br>
                <input id="phone" style="margin-top:5px;" name="telephone" type="text" required><br>
                <input class="bouton_submit" type="submit" name="user_send_registration" value="S'inscrire" style="background-color:#3498db; color:white; width:100px; height:35px;">
        </form>
        <?php
        return ob_get_clean();
}
add_shortcode( 'register', 'registration_form' );

my wordpress page:

<!--my shortcode-->
[register]

<script>
function getIp(callback) { fetch('https://ipinfo.io/json?token=<your token>', { headers: { 'Accept': 'application/json' }}).then((resp) => resp.json()).catch(() => { return { country: 'fr',};}).then((resp) => callback(resp.country));}
   const phoneInputField = document.querySelector("#phone");
   const phoneInput = window.intlTelInput(phoneInputField, { preferredCountries: ["fr", "us", "uk"], utilsScript: "https://cdnjs.cloudflare.com/ajax/libs/intl-tel-input/17.0.8/js/utils.js",});
</script>
<script>
$("#registration_form").validate({
rules:{
   nom:{required:true}, 
   prenom:{required:true}, 
   mail:{required:true, email:true, emailExt:true}, 
   login:{required:true}, 
   mdp:{required:true}, 
   mdp2:{required:true}, 
   societe:{required:true}, 
   fonction:{required:true}, 
   adresse:{required:true}, 
   complement:{required:false}, 
   ville:{required:true}, 
   code:{required:true}, 
   pays:{required:true}, 
   telephone:{required:true, minlength: 10, maxlength: 15, number: true} 
}, 
submitHandler: function(form) {
    if(isReqInprogress){
        return;
       }
        $.ajax({
        url:"/wp-content/themes/themename/process.php",
        type: "post",
        data:$('#registration_form').serialize(),           
        dataType:"JSON",
        success: function(response) {
            alert("Your message has been received and we will be contacting you shortly to follow-up.");
            isReqInprogress = false;
        }
    });
}
});
</script>

And then my process.php file:

<?php
define('BLOCK_LOAD', true);
require_once( $_SERVER['DOCUMENT_ROOT'] . '/wp-config.php' );
require_once( $_SERVER['DOCUMENT_ROOT'] . '/wp-includes/wp-db.php' );
$wpdb = new wpdb( DB_USER, DB_PASSWORD, DB_NAME, DB_HOST);

global $wpdb;
$data = $_POST;

$form_url = wp_get_referer();

$query = $wpdb->insert('wp_clients_user',
        array(
                'nom'                => $data['nom'],
                'prenom'             => $data['prenom'],
                'email'              => $data['email'],
                'login'              => $data['login'],
                'mdp'                => $data['mdp'],
                'societe'            => $data['societe'],
                'fonction'           => $data['fonction'],
                'adresse'            => $data['adresse'],
                'complement_adresse' => $data['complement'],
                'code_postal'        => $data['code'],
                'ville'              => $data['ville'],
                'pays'               => $data['pays'],
                'telephone'          => $data['telephone'],
                'actif'              => false
        ),
        array(
                '%s',
                '%s',
                '%s',
                '%s',
                '%s',
                '%s',
                '%s',
                '%s',
                '%s',
                '%d',
                '%s',
                '%s',
                '%d',
        )
);

if ($query) {
        $response['error'] = "true";
}else{
        $response['error'] = "false";
}
echo json_encode($response);
        // $wpdb->show_errors();
// Redirect  user to the welcome page if everything is okay
wp_safe_redirect(wp_siteurl);
exit();
?>

I forgot to mention it but process.php and functions.php are in the same folder, located at /wp-content/themes/industrial-child/

Thanks for the help.