If you copy /themes/hyde/layouts/partials/sidebar.html or any other theme file, you can place it in the equivalent place in your project, and hugo will use that instead. So, copy that file to /layouts/partials/sidebar.html and edit that.
Thank you all for your replies. I took the easy way, adding in my sidebar.html :
<p class="lead">
{{ with .Site.Params.description }} {{.}} {{ else }}Je suis aussi sur twitter <a href="http://twitter.coxxxxxx">@arxxxxx</a> et <a href="httxxxxxxxxxxxxxx">wechat</a>. On peut m'écrire à arnauld@xxxxxxxx{{end}} ou sur l'IRC : <a href="ircs://irc.geeknode.org">Arnob</a> at Geeknode.</p>