What you are describing is the Splash Page.
The Splash Page is an image placeholder for the gallery which, when clicked, will expand the gallery to fill the browser viewport (to give the gallery as much room as possible).
By default, the Splash Page will be displayed on mobile devices when a gallery is embedded in a web page alongside other content (where the gallery might be too small to use).
Check out the Gallery Tour where there is a short section about the Splash Page.

Please check out the Splash Page configuration options here.

By default, Juicebox uses the first image in the gallery as the Splash Page image. You can change this if you like via the splashImageUrl option (in JuiceboxBuilder-Pro's 'Customize -> Splash Page' section).
You could also choose to not use the Splash Page at all by setting showSplashPage="NEVER".

Whether you use the Splash Page or not, on a mobile device, the gallery will be displayed in Small Screen Mode (check out the Gallery Tour link above for details) where thumbnails and main images are displayed on separate pages (to give the main images more room).
If you'd rather have the gallery displayed in Large Screen Mode (where thumbnails are displayed alongside the main images) on all devices and in all browsers, then you can set screenMode="LARGE" (in JuiceboxBuilder-Pro's 'Customize -> General' section).

Your gallery currently sets maxCaptionHeight="70".
Try increasing the maxCaptionHeight (at least to the default value of 120) to give your captions more room. You'll find maxCaptionHeight in JuiceboxBuilder-Pro's 'Customize -> Caption' section.

Also, your gallery's first caption is:

<caption><![CDATA[</font><font color="#CCCCCC">Projet: Pecquencourt - Production: <font color="#0066FF"><a href="https://mw-architecture.fr/">MW Architecture </a><font color="#CCCCCC"> - Date: Novembre 2022  </font><br><font color="#0066FF"><a href="http://www.vincefx.com">www.vincefx.com </a><font color="#CCCCCC"> vincefx@free.fr tel:06.98.72.06.93]]></caption>

For a valid HTML 5 page, I'd recommend changing <font> tags for equivalent <style> tags as noted here (a little bit of work would be required but the resulting code would be HTML 5 compliant). Also, there's no need to start the caption with a closing </font> tag and you're missing a few </font> tags throughout your caption text.

Your gallery's embedding page actually has two galleries embedded into it (two lots of embedding code with with same 'juicebox-container' id).
I expect that you're just trying to embed one gallery so you should be able to remove one set of embedding code.
If you are trying to embed multiple galleries into a single web page, then you only need to load the 'juicebox.js' JavaScript file once per page (not once per gallery) and each gallery should be loaded into a <div> with a unique id.

I hope my notes above point you in the right direction.

At the moment, your gallery looks good in both portrait and landscape orientations in Mobile Safari on my iPhone and in Mobile Chrome on an Android device.
If things look a little odd, then try clearing your browser's cache before reloading your gallery's web page to see if this helps to resolve the problem.

It's usually a good idea to set screenMode="AUTO" (the default value) and allow Juicebox to determine whether to display the gallery in Large Screen Mode or Small Screen Mode (depending on the device being used to view the gallery).

In Small Screen Mode (whether you are in Fullscreen Mode or not), you can display the Thumbnail Button on the gallery's Button Bar (to allow the visitor to view the thumbnail pages) by setting showSmallThumbsButton="TRUE" (in JuiceboxBuilder-Pro's 'Customize -> Thumbnails' section).
You will need to display the Button Bar in your gallery, though, in order for the Thumbnail Button to be displayed (and your gallery currently hides the Button Bar by setting buttonBarPosition="NONE").

Your first image's caption is currently the following:

</font><font color="#CCCCCC">Projet: Pecquencourt - Production: <font color="#0066FF"><a href="https://mw-architecture.fr/">MW Architecture </a><font color="#CCCCCC"> - Date: Novembre 2022  </font><br><font color="#0066FF"><a href="http://www.vincefx.com">www.vincefx.com </a><font color="#CCCCCC"> vincefx@free.fr tel:06.98.72.06.93

You could change it to this to be HTML 5 compliant:

<p><span style="color: #cccccc;">Projet: Pecquencourt - Production: </span><a href="https://mw-architecture.fr/" style="color: #0066ff;">MW Architecture</a><span style="color: #cccccc;"> - Date: Novembre 2022 </span><br><a href="http://www.vincefx.com" style="color:#0066ff;">www.vincefx.com</a><spa style="color: #cccccc"> vincefx@free.fr tel:06.98.72.06.93</span></p>

This is HTML 5 compliant but it might not make a visible difference. Most browsers will likely still render the <font> tag OK and may be quite tolerant towards things like missing end tags.
If you don't see a visible difference, then you might not want to bother changing all your captions just now (as it is quite a large task) but it would be a good idea going forward (especially as your web page uses the HTML 5 Doctype Declaration).

Yes. The embedding page is your 'ImagesArchi.html' file.

I never actually saw two galleries on the page but there were two sets of embedding code (both embedding the same gallery into the same container).
Your web page only has one set of embedding code now, so that's good.

Your gallery's Button Bar displays OK in my own desktop browsers and on my Android phone.
If you don't see the Button Bar yourself, then try clearing your browser cache before reloading your gallery's web page to ensure that the browser is loading the gallery's 'confg.xml' file fresh from your web server (with the new setting for buttonBarPosition) instead of using an older, cached version.

Incidentally, on mobile in portrait orientation, there's not much room for the Button Bar (due to the length of the Gallery Title) so the Button Bar spills over onto several lines. Try shortening the Gallery Title.
Also, in Small Screen Mode (on mobile devices), please note that the Button Bar is displayed only on main image pages and not on thumbnail pages.

You're welcome! I'm glad you've got it working. Thanks for letting me know.

@fabienismyfriend

Your galleries seem to be working as expected when I view them on mobile devices.
If a mobile device has been detected and the gallery is embedded on a web page with dimensions of less than 100% x 100% or if there is other content on the page (i.e. if the gallery is not the only element on the page and does not take up the full page), then the Splash Page will be displayed.
The Splash Page is a placeholder for the gallery which, when tapped, will expand the gallery on a new page of its own (to give the gallery more space).
By default, the Splash Page displays the first image in the gallery. You can change this to any image you like using the splashImageUrl configuration option (in JuiceboxBuilder-Pro's 'Customize -> Splash Page' section).

There are a few things you could try.

(1) If you simply do not want the Splash Page to appear, then you can set showSplashPage="NEVER" ('Customize -> Splash Page').
(2) Additionally, if you want the Large Screen Mode version of your gallery to be displayed on all devices, then you can set screenMode="LARGE" ('Customize -> General') but please bear in mind that some gallery elements may appear too small on mobile devices.

You could avoid the problem by ensuring that your gallery is the only element on your web page and that its dimensions are 100% by 100%.
Currently, your gallery has a height of 92% and there is a table on the page alongside the gallery.
If you were to remove the table and change the height of the gallery to 100%, then the gallery would fill the page and the Splash Page would not appear (but the gallery would still be displayed in Small Screen Mode on mobile devices which would be beneficial when viewing on small screens).

I'd recommend using the 'index.html' page from a gallery built with JuiceboxBuilder-Pro as a template (where the gallery is the only element on the page).

Also, if you check your current gallery's embedding page with the W3C Markup Validation Service, you'll see that there are some HTML errors on the page (such as a missing </body> tag at the end of the file). The info entries do not need attention but the errors really ought to be fixed.
If a web page does not contain valid HTML code, then the web page might be rendered by the browser in an unpredictable manner. Some browsers are more tolerant towards errors than others but if the code on the page is valid (i.e. no errors), then you can be sure that the page will display with consistency across all browsers.

I hope these notes point you in the right direction.

This has to be true in order for the Splash Page to not be used on a mobile device without explicitly setting showSplashPage="NEVER".

The Splash Page is used on mobile devices in 'New 1' because the gallery is not 100% x 100% and there is another element on the page (a <header>).

The Splash Page is not used on mobile devices in 'New 2' because the gallery is 100% x 100% and there are no other elements on the page.

The gallery displays in Small Screen Mode when viewed on mobile devices (thumbnails and images on separate pages).  You can navigate between images by swiping left or right and you can view the thumbnail page by tapping the Thumbnail Button on the Button Bar. Please see here for more information about Screen Modes.

The gallery goes straight to the first image in the gallery because you have set firstImageIndex="1" in your gallery's 'config.xml' file. If you remove firstImageIndex="1" from your gallery's 'config.xml' file, the gallery will initially display the thumbnail page (rather than the first image in the gallery).

I hope these notes help to clarify things a little.