France can project enough power that far if Austria's on their side. Also Russia wasn't the one who had troops in the Sejm to elect the past 2 Kings, that was Austria.
And I think you're vastly overestimating the Russian Army of this period. Russia would not be able to beat Austria so easily, it took them 6 years to beat the Ottomans in the Same time Period and Austria had a better army than the Ottomans at this time. Also, if Austria and France are backing a Wettin, which is likely, they'll have Maurice de Saxe as their Field Commander. Maurice was a bonafide military genius. Russia doesn't have a commander to match him.
Um...by the time the Polish throne is in question, Maurice de Saxe is dead.
That said, I've always kind of liked the idea of somehow, that when Friedrich Christian dies, his brother, Prince Xavier, succeeds as king of Poland. They were iffy about electing Friedrich Augustus III due to it would require a regency, but Xavier would have no such problem. If Austria and France can be persuaded to support him, chances are Russia will either pick some other native candidate (Czartoryski, Branicki, Lubomirski),
or reach an agreement with Xavier to support his election (while maintaining a British-Prussian alliance in all other aspects).