France is not England!!!
I swear every time this comes up the members of this site are ready to kill King Louis by every means imaginable, INCLUDING WILD DOGS!
Sorry to rain on your collective bloodlust, but the French people would never tolerate the killing of a King or Dauphin, ever. It's ASB, period.
It almost happened IOTL, though. Hell, in fact, there were quite a few people who wouldn't have given two shits if the royals had been murdered by the time the Flight occurred. In fact, there were riots for several days straight after they were restored.....not to mention an assassination attempt on Count Von Fersen himself! And after the Bourbons were *finally* thrown out for good in 1847(Albeit mostly non-violently this time), why do you think that the HRE was (bloodily) dismantled and stomped into the dust after they lost the Pan-European War(by that point, even the Russians thought they were bad news!)? There was a *lot* of resentment that had built up against the old royal families up until then, and it wasn't just going to magically disappear.
(Interesting fact, btw: Crown Prince Conrad, supposedly a great nephew by marriage of Count von Fersen, and who would have been second in line for the HRE's throne at the time of its dismemberment, emigrated to the U.S. temporarily after his exile, where he later offered his services to the Confederacy during the Civil War.....as did many other exiled German noblemen who arrived in the U.S. south of the Ohio; he apparently viewed the C.S.A. as an anti-revolutionary reaction, as it were, against the supposed "tyrant", William Garrison, in Washington.....this, despite Garrison being one of the most libertine Presidents of the era.....or perhaps *because* of that, maybe.)
Whereas the assassination of Ernest Augustus in 1846 genuinely horrified many Britons, despite his incredible unpopularity, and his killers were all sentenced to very long jail terms(and one man executed!) after Caroline's succession was made clear.