Complete French victory in the War of Spanish Succession. Phillipe d'Anjou succeeds the Sun King: he now rules France, Spain, and about half each of Italy and the Low Countries; plus vast territories in the New World and elsewhere.
Then, in an alt-Austrian Succession war, the French advance a claim to the remaining Habsburg territories of Austria, Bohemia, and Hungary, plus the Imperial Crown, denying *Maria Teresa* the throne. They are supported by Prussia, Russia, Bavaria, and Denmark; opposed by Austria o/c, Saxony-Poland, Sweden, Britain, the Netherlands,and Portugal. Bavaria gains Tyrol and Prussia Silesia; the rest goes to the Bourbons. Sweden stalemates her foes; Britain, Holland, and perhaps Portugal make minor gains overseas.
In the aftermath, the Pope crowns the the king (Louis XV, perhaps), Holy Roman Emperor. In Italy and South Germany, Bourbon power is almost uncontested. Prussia is now tied to the Anglo-Dutch-Hanoverians, who are the main opponents of Paris and may be in personal union. This renders Sweden an ally of France, and therefore Denmark and Russia are in the opposition.
Then the Elector of Saxony dies. The Emperor is elected to the Polish throne by the Sjem, and little Saxony cries foul.
Now, the French-dominated Holy Roman Empire (including significantly autonomous minor partners Bavaria, Savoy, and the Papal States) and Sweden are at war with Britain-Netherlands-Hanover, Prussia, Denmark, Russia, and Saxony. Portugal and Turkey may also join this coalition at some point; if Turkey joins, Venice and/or Persia may well support France. Alternately, the Ottomans could ally with France and attempt to expand in Georgia. The Americas and India will also be major theaters in this war.
This third Succession war (War of Polish Succession) may be decisive. Either the Bourbon-Catholic bloc will finally be contained or even severed; or, France could finally establish herself as utterly dominant from Cadiz to Minsk and from Malta to Kiel. Incidentally, this may well be the war where the Fleur de Lis flies above the Kremlin for a period. Italy and Germany (or at least Catholic Germany) would slowly loose their independent identity from the Empire. Only the fringes of Europe- Portugal, Britain, Holland, Scandinavia, perhaps Prussia, Russia, and Turkey - would remain outside the French sphere.
Where do we go from here? Paris is hegemonic but several plausible foes still exist. Does this Europe enter a Golden Age free from war with France replacing the UK as top dog and Britain and Russia serving as seconds? Or does the period of great wars continue uninterrupted?
Note, incidentally, that while this scenario leaves Frances dominant in Europe, the Americas, India, and the Indies may be much more interesting and even tend to favor her foes, within reason.