Hi,
OK, so it’s not the Browsers and it’s not the themes.
I thing Rencontre is clear too (except the choice to keep the same name when you change the photo, but it’s a technical choice).
Now, what about your host (server/htaccess) and your WordPress (installed by yourself or your host ?) :
Try to display the photo directly from your theme. Edit the index.php from your theme and add, after the body tag, the image tag :
<p>*** T E S T ***</p>
<img src="https://my site/.../abcd.jpg?r=<?php echo rand(); ?>" alt="photo" />
Regards