While There are numerous threads on la Grande Mademoiselle marrying Charles II of England, I don't think I've seen one on this topic; a marriage to the man she rejected the exiled Stuart monarch for, Emperor Ferdinand III. From the death of Ferdinand's first wife in 1646 to his third marriage in 1651, Mademoiselle was obsessed with an Imperial match that would transform her into the First Lady of Christendom. Now from what I've read in La Grande Mademoiselle at the Court of France by Vincent J. Pitts there was some serious considerations towards such a match before Ferdinand married Maria Leopoldine of Austria-Tyrol.
So lets say that the French tie Mademoiselle's marriage to the Emperor to the peace negotiations at Westphalia and the match go's forward. How would a French Empress in Vienna affect things? Would we see closer relations between Paris and Vienna? Could a French branch of the Habsburgs emerge as Princes étranger at Versailles? How would this effect the strained Imperial finances?