Thank you sooooo much. It works now. The problem was coming from another plug-in. The BPS plug-in was not the problem indeed. I will follow all your recommandation. Thank you so much for providing so good support!
I just removed the BPS to test but the problem remains so I will reinstall it.
Many thanks for your reply. Here is the link: http://www.francoisgoet.eu
I forgot to mention that my website is not too heavy. It takes only 3% and each images are using a small size format (less than 100ko). And it was working very well for many weeks! Thanks a lot if you read me and can help!