I think that you should try to catch a glimpse of this website http://www.lyon.fr/vdl/Localizer/changeLanguage?lang=en&goto=http://www.lyon.fr/vdl/sections/en/ and you also can try to send a mail if you find an email adress on it. If you want your mail to be traduced in French I guess that we can help you.

I hope that you will succeed in your search, but maybe you should ask more informations about him to your friend; you are not obliged to tell her the truth, that you are seeking for her grandfather etc... But maybe you can say something like "I heard about a French politic Olivier Besancenot (or else) and ask her if she is related to him and if not what is the name of her grandpa.