It looks like there is a misbehaving wp-config.php, plugin, or theme on your site.
If you go to http://www.the-nappyberry.fr/xmlrpc.php , you'll see a message saying "XML-RPC server accepts POST requests only." That's the correct message. The problem is that there are other elements above the message: an extra blank line. This extra space is annoyingly important. It suggests that some plugin, theme, or wp-config.php file in your WordPress has extra "whitespace" (new lines, spaces, tabs, ...) before the first "<?php" in the file. This problem is another symptom of a more common problem: the "Headers already sent" problem: http://codex.wordpress.org/FAQ_Troubleshooting#How_do_I_solve_the_Headers_already_sent_warning_problem.3F
Can you check your wp-config.php, theme files, and plugins for such whitespace?
Once you've fixed that whitespace, try connecting Jetpack again; you should be able to. If you can't, let me know. If you *can*, great!