How can I complete a Django form field with a date selected in a Flatpickr calendar?

Question

I'm beginning to build a website using Django and I've ran into some issues when trying to update a database. More specifically, I want to use a Flatpickr calendar so that the user can select a date and time and then use that information to populate the "date" field in my form, but I don't know how to do this. I know I could just use a date-time widget for the form field and make it simpler, but I want to use Flatpickr to make it look nicer. I've tried updating the field with JavaScript but it didn't work.

I copy here a section of the code so you can see what I've tried.

First, a piece of the HTML file:

<script>
        var calendar = document.getElementById("div_calendar")
        flatpickr(calendar, {
          enableTime: true,
          dateFormat: "Y-m-d H:i",
          inline: true,
          appendTo: calendar,
          onChange: function(selectedDates, dateStr, instance) {
            
            
            if (selectedDates.length > 0){

                //We obtained the first date selected (we assume there is only one)
                var dateSelected = selectedDates[0];

                // Format the date as a string with the format 'Y-m-d H:i'
                var formattedDate = dateSelected.toISOString().slice(0, 16).replace('T', ' ');

                // Update the value of the form field
                $("#{{ form_bookings.date.id }}").val(formattedDate);
            }
                        
          }
        });
      </script>
    
    <div id="div_appointment">
        <h2 id="h2_appointment">Book your appointment</h2>
        <form id="form_bookings" action="" method="POST">
            {% csrf_token %}

            {{form}}
                        
            <input type="submit" value="Aceptar">
        </form>
    </div>

The file where I declared the model to use with the form:

from django.db import models
from django.utils import timezone

class Bookings(models.Model):
    name = models.CharField(max_length=50)
    last_name = models.CharField(max_length=50)
    email = models.EmailField(max_length=50)
    date = models.DateTimeField()

And finally, the code of the file where I declared the form:

from django import forms
from .models import Turnos

class FormBookings(forms.ModelForm):
    class Meta:
        model = Bookings
        fields = "__all__"