Richelieu was giving aid to Protestants such as Sweden during the Thirty Years War because it was kind of a "enemy of my enemy" mentality because they hated Protestants. But they had a historic rivalry with the Habsburgs since I believe the Habsburg-Valois War. So if Richelieu was excommunicated, he could possibly just have everyone in France convert to Protestantism as there were and are still a lot of Catholics in France. And since religion was used as a certification of power in this time period, it is certainly plausible that such a switch could occur, similar to what Henri IV did in France after the French Wars of Religion when he was Protestant and converted to Catholicism or the host of German princes that converted to Lutheranism during the Reformation so they could acquire church land. The pope did not want one of his biggest support groups to get up and leave.