JSFiddle - React, Tailwind, and code Playground

HTML

<body>
<input id="MailClient" class="form-cadre" name="MailClient" type="email" placeholder="Exemple : [email protected]" title="Remplir ce champ est nécessaire pour que je puisse vous répondre" />
</body>

CSS

jQ("#email").focusout(function retest() {
        //var form = document.forms["adminForm"];
        var rtest = new RegExp ("/^[a-z0-9._-]+@[a-z0-9._-]+\.[a-z]{2,6}$/");
        //var check = true;
      if(!rtest.email(this.value)){
                jQ("#email").css("background-color","rgb(245,62,84)");
                return false;
              }
              else{
                jQ("#email").css("background-color","green");
                return true;
              }
      });

JavaScript

$("#MailClient").focusout(function() {
    var myRegex = /^[a-z0-9._-]+@[a-z0-9._-]+\.[a-z]{2,6}$/;

    if(!myRegex.test(this.value)){
                $('#MailClient').css("background-color","rgb(245,62,84)");
                return false;
              }
              else{
                $('#MailClient').css("background-color","green");
                return true;
              }
            });