The problem is also happening on the Prestashop demo site at: http://demo.prestashop.com/en/?view=front
Just make your browser window narrower until when the Message box drops below the button fields. When the window is at its widest width (with the Message box still below the button fields) - then try to click on the Attach File button. It doesn't work, but if you click on the right side of the page across from it in the blank area then it works.
If I could paste a screenshot on here I could show you the problem, but I can't figure out how you upload images to this forum.