I want to contribute an answer here as I too have faced the same issue - we want the $_FILES element available as part of the same post as another form. My answer is based on @mrtnmgs however notes the comments added to that question.
Firstly: Dropzone posts its data via ajax
Just because you use the formData.append option still means that you must tackle the UX actions - i.e. this all happens behind the scenes and isn't a typical form post. Data is posted to your url parameter.
Secondly: If you therefore want to mimic a form post you will need to store the posted data
This requires server side code to store your $_POST or $_FILES in a session which is available to the user on another page load as the user will not go to the page where the posted data is received.
Thirdly: You need to redirect the user to the page where this data is actioned
Now you have posted your data, stored it in a session, you need to display/action it for the user in an additional page. You need to send the user to that page as well.
So for my example:
[Dropzone code: Uses Jquery]
$('#dropArea').dropzone({
    url:        base_url+'admin/saveProject',
    maxFiles:   1,
    uploadMultiple: false,
    autoProcessQueue:false,
    addRemoveLinks: true,
    init:       function(){
        dzClosure = this;
        $('#projectActionBtn').on('click',function(e) {
            dzClosure.processQueue(); /* My button isn't a submit */
        });
        // My project only has 1 file hence not sendingmultiple
        dzClosure.on('sending', function(data, xhr, formData) {
            $('#add_user input[type="text"],#add_user textarea').each(function(){
                formData.append($(this).attr('name'),$(this).val());
            })
        });
        dzClosure.on('complete',function(){
            window.location.href = base_url+'admin/saveProject';
        })
    },
});