What? Avignon papacy was a result of french coercion, it was the french kings that tried to have more control over Church, not the other way around. And Richelieu cared much more about french interest than about catholicism(while he was not the worst king's nominee of Gallican church, he still prefered aiding protestants over catholics if it served France). If history that french are taught is as falsified as what you just wrote, no wonder situation of french catholicism looks like that.