IDK, Charles' position as governor-general was at first by right of his wife being the only surviving sibling of MT. Then after she died in childbirth, he took over as Governor-General simply because of a lack of other Habsburgs to fill the post. OTL he never remarried after his wife's death, reportedly telling his sister, the abbess of Remiremont (Anne Charlotte de Lorraine) that 'there is no point in remarrying for what will my children inherit?' when she berated him for his long-standing affair with the mother of one of his bastards. And Josef II used the reasoning to nullify Charles' will (he was/became pretty wealthy OTL (the Habsburg-Teschen wealth comes in part from him)), by saying that Charles, as a member of the Imperial Family, had not obtained imperial consent when making his will, and so it was null and void.
Now, this would need a POD (possibly after the marriage of François III to Maria Theresia in 1736 when the duchy was renounced, but before Charles' marriage to Maria Anna in 1743). Perhaps his mother, who was against the signing away of the duchy (she was willing that François renounce it to Charles, but not renounce it completely), a French princess by birth and cousin to Louis XV, is more successful in persuading her youngest son to go to Paris instead of Vienna. That said, though, if the French match mentioned above goes through, the Viennese impression of François as a spying French coward (there were quite a few puns made on his name in German 'Franz' and the German for French 'Franzoischer' concerning their dislike of him), will be still greater.
And even if Charles accepts the pension and position at Versailles, its a long jump from 1740s Europe to Belgian Independence of the 1790s (Brabant Revolution)/1830s