If you would like to manually embed a Juicebox gallery in a Drupal page, I would recommend using the baseUrl method of embedding as documented here.

Essentially, you would create a gallery with JuiceboxBuilder-Pro, upload the entire gallery folder (not just the contents) to your web server and paste the baseUrl embedding code into your web page.
It does not matter where you upload the gallery folder to on your web server as long as the paths within the embedding code (the path to the 'juicebox.js' file and the baseUrl itself) are correct.

You do not need to upload your gallery folder to a location within your Drupal installation and you do not need to use the Juicebox files from their location within the Drupal module (although you can if you like).

For example, if you have a gallery folder named 'my_gallery_folder' and you upload the entire folder to the root directory of your web server (into your 'public_html') folder, then the embedding cdoe you would use would look something like this:

<!--START JUICEBOX EMBED-->
<script src="/my_gallery_folder/jbcore/juicebox.js"></script>
<script>
  new juicebox({
    baseUrl : '/my_gallery_folder/',
    containerId : 'juicebox-container',
    galleryWidth : '800',
    galleryHeight : '600',
    backgroundColor: '#222222'
  });
  </script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

To directly answer your query above, there are a few problems with the code you use.
(1) If using an absolute URL, it should start with 'http://'.
(2) The 'public_html' folder name does not form part of the publicly accessible path.
(3) Your baseUrl line of code should have a comma (',') after it as there are further configuration options after it.

Therefore:

<script src="www.joaqimb.be/public_html/sites/all/libraries/juicebox/juicebox.js"></script>

... would become:

<script src="http://www.joaqimb.be/sites/all/libraries/juicebox/juicebox.js"></script>

... and:

baseUrl : "www.joaqimb.be/public_html/sites/all/libraries/juicebox/classic/img/Juicebox Namur"

... would become:

baseUrl : "http://www.joaqimb.be/sites/all/libraries/juicebox/classic/img/Juicebox Namur/",

Rather than using absolute paths, I would recommend using the leading slash notation (to denote your root directory) rather than hard-coding the 'www' subdomain into your patsh so that your galleries display on both www.joaqimb.be and joaqimb.be.
Try using the the following lines of code in your embedding code:

<script src="/sites/all/libraries/juicebox/juicebox.js"></script>

baseUrl : "/sites/all/libraries/juicebox/classic/img/Juicebox Namur/",

Having uploaded your entire gallery folder, the embedding code is all you need.
It looks like the problem is that your gallery folder is named 'Juicebox Namur' but the two paths in your embedding code use 'Juicebox_Namur' (notice the underscore instead of a space). Make sure that the name of the gallery folder in the paths in your embedding code matches the name of the gallery folder on your web server.

Please post the URL to your web page so that I can take a lok and help further.
Once I see the code that you are using on your web server, I should be able to determine the cause of the problem.

I have taken a look at your web site and have found your gallery's web page.
The problem is that you have entered your embedding code into your Drupal editor as plain text and not as HTML code (and the embedding code is appearing as text on your web page rather than being rendered as actual HTML code by the browser).
You will need to change your editor's 'Text format' (at the bottom of the editor) from 'Plain text' to 'Full HTML' before entering the embedding code.

This is not the problem (see above) but you can change the name of the page to anything you like (to avoid filename conflicts).
If you are embedding your gallery in an existing web page, then you do not need to use (or upload) the gallery's own 'index.html' file at all. It is used only if you want to display the gallery on a page of its own.
Also, the 'index.html' file will be stored within the gallery folder and if you use a baseUrl, you will upload the entire gallery folder (not just the contents) so there is no chance that the gallery's 'index.html' file will conflict with one of your own 'index.html' files.

On your web server, the root directory is 'public_html'.
If you upload a file named 'test.html' to your 'public_html' directory via FTP, then it will be accessible on the web at '/test.html' in one of your web pages.

This fails within the forum software because you use a space in your 'Juicebox Namur' folder name (and the forum software sees a space as the end of the path). As long as the paths are correct within your web page, everything should be OK.
However, I would recommend that you use only web-safe characters for files and folders on your web server.
Please see section 2.3 of this document for details.