After his uncle died in 1729 and Franz Ludwig, Archbishop-Elector of Trier, succeeded him after vacating his own see, Franz Georg was unanimously elected the new Archbishop of Trier and thus appointed Prince-Elector of Trier.
In 1729, following the passing of his uncle, Franz Ludwig succeeded him as Archbishop-Elector of Trier. As a result, Franz Georg was elected unanimously as the new Archbishop of Trier and consequently appointed as the Prince-Elector of Trier.