JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
<script src="https://code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
  <p><input type="radio"  id="nom" name="search_by" value="nom" checked>Nom</p>
  <p><input type="radio"  id="ville" name="search_by" value="ville" >Ville</p>
 
<form method="POST">
<input type="text" id="txtAllowSearch" class="selector" name="label">
<input type="hidden" id="txtAllowSearchID" name="id">
<input type="submit" value="envoyer">
</form>

JavaScript

function search_by(){
valeur = $('input[name="search_by"]:checked').val(); 
alert('selection : '+valeur)
}
 
$(function(){
 
 $('[name="search_by"]').on('click', search_by);
var valeur='nom' ;
 

$('.selector').autocomplete({
  delay:100, //delais en milisecondes
  minLength: 2, //longueur minimum du texte
    source: './source.php?search_term='+valeur,
    select: function (event, ui) {
      event.preventDefault()
        $("#txtAllowSearch").val(ui.item.label); // display the selected text
        $("#txtAllowSearchID").val(ui.item.id); // save selected id to hidden input
    }
});
});