He began his career as a soldier in the French service.
He went to the court of the elector of Cologne at the same time as his brother, Franz Egon, whose zeal for the cause of Louis XIV of France he shared. In 1672 the intrigues of the two Fürstenbergs had resulted in a treaty of offensive alliance between the French monarchy and the electorate of Cologne, and, the brothers being regarded by the Imperialists as the main cause of this disaster, William was seized by imperial soldiers in the monastery of St Pantaleon at Cologne, hurried off to Vienna and there tried for his life. He was saved by the intervention of the papal nuncio, but was kept in prison till the signature of the Treaty of Nijmwegen (1679).
As a reward for his services Louis XIV appointed him bishop of Strassburg in succession to his brother in 1682, in 1686 obtained for him from Pope Innocent XI the cardinal's hat, and in 1688 succeeded in obtaining his election as coadjutor-archbishop of Cologne and successor to the elector Maximilian Henry. At the instance of the emperor, however, the pope interposed his veto; the canons followed the papal lead, and the progress of the Allies against Louis XIV in the Nine Years War deprived him of all prospect of success, William Egon retired to France. He retired to his abbey of St-Germain-des-Prés near Paris, where he died on April 10 1704.