Louis XVI, Marie Antoinette and the royal family were fleeing to the town of Varennes
The intended destination of the royal family was actually the royalist fortress of Montmedy.
Louis XVI intended to flee France
Louis XVI firmly refused to leave the country and, according to biographers such as Fraser, Webster, Hardman and more, turned down several flight routes to Montmedy which would have been much faster and safer because they briefly took him across the French border.
The coach which carried the royal family was recognized because it bore their royal arms/was too extravagant
The coach, presumably ordered by Axel Fersen, was large but not unusually so and was in fact based upon previously drafted plans for a Parisian’ companies carriage. It was not decorated with the arms of the royal family and, on the outside, was nothing out of the ordinary. The coach featured a variety of traveling amenities often used by those who could afford them - including a larder, cooker, fold-up table and chamber pots - because it was necessary for the flight to eliminate the need for its passengers to stop or leave the carriage.
The heaviness of the coach, both because of its luggage and the number of passengers, did present some problems during the escape attempt. It required more frequent changes of horses and meant that the coach traveled at about six to seven miles an hour—a steady pace, but a lighter coach could have meant a faster and potentially more successful escape. However, the reasons for the cumbersome coach are understandable, if not from a political point of view then a human one. Politically, Louis XVI (at least) expected that after his flight, he would be able to greet his subjects as their king and rally them around his cause - hence the inclusion of his crown and royal robes in the baggage. Also included were clothing for the royal family and the Queen’s now-infamous case, which doubled as an elaborate picnic basket (it included dinnerware) and a dressing case.
But the size was more than a result of political maneuvering: After some discussion of separate flight attempts, Louis XVI and Marie Antoinette adamantly refused to be separated from each other and from their children. The comte and comtesse de Provence, who escaped the country on the same day, traveled in small coaches separately and were able to quickly flee. But the king and queen and, eventually, Madame Elisabeth vowed not to take the risk of being separated, should one or more parties be captured.
It’s very important, however, to note that even though the size of the coach and its amenities had an influence over the coaches speed, they were not the cause of the flight’s failure. The first stumbling block occurred when the harness of the carriage broke—bad luck and nothing unusual for travel at the time, but it caused a chain reaction. The mending of the harness caused the coach to become 2 hours behind schedule (it was already running late) which, in turn, caused the duc de Choiseul (who was waiting at a point with dragoons) to take his men back toward Montmedy, which meant that there would be no military escort waiting for them if (in reality, when) they needed it.
The royal family was recognized because of a coin which bore Louis XVI’s face/Marie Antoinette’s perfume
While both make for excellent legends, there is no evidence that Drouet, who was an official of the post at Sainte-Menehould, actually recognized the king because of a coin or any money which bore the king’s profile. The idea that the family was recognized because the post masters at Varennes smelled the queen’s perfume (although it was included in her luggage) is another colorful story, among the same lines as those that turn the ordinary carriage into a royal folly on wheels.
Euh, non, en fait, deux et trois ne sont décidément pas de mythes, surtout pas deux, puisque Louis n’aurait pas eu les troupes promises de son beau-frère l’empereur d’Autriche s’il ne franchissait pas la frontière. Déclarer que quelque chose est un mythe ne fait pas qu’elle le soit.
"Uh, no, actually, two and three are decidedly not myths, especially not two, as Louis would not have the troops promised his brother the Emperor of Austria if he did not cross the border . Declare that something is a myth is not that it is."
There is no evidence that they ever intended to cross the border and certainly not in exchange for Leopold’s troops, which he wanted to be paid for due to the “expense of moving them” to the border. Three is, again, a myth. The carriage was not recognized because it had royal arms - it was plain green - and it was not recognized or unusual because of its size, which was large but not unheard of.