Login to your admin page on Wordpress, go to your Homepage and re-link the images. It looks like the image attribute for src (the bit that will show the images) has no image URL in it.
It is showing the ALT tag description, but you might have to re-link the images correctly again.
thanks a lot for helping me. In fact, the homepage is a huge portfolio showing several frontpage image (one per portfolio). I made you a printscreen of the first portfolio. As you proposed, I deleted the small image put in front and replaced it by a new one hoping that the src would present the image URL but it is not the case.