Even Miriam Webster has a note that Americans mistakenly use it for main course (completely incorrectly) because French sounds fancier.
https://www.merriam-webster.com/dictionary/entr%C3%A9e#:~:te...
Including entrée, incidentally, which gave us the entrée and the entry.
Even in France, in the context of elaborate multiple course meals, the entrée eventually stopped being the very first thing that was served. Soup started to take that spot, and gave us what we now call the appetizer, which used to be chiefly soup or salad but now could be almost anything.
For those elaborate meals, the entrée was just the first course of the multiple courses that were the "main" dish.
Separate main courses have largely fallen out of fashion, and they collapsed into one plate with a serving of each. This is still the entrée in the US and Canada, and that makes perfect sense, given the history.
So no, it wasn't just that it sounded fancier.
That meaning is also accepted by the French Academy nowadays:
Fig. En parlant d’une période de temps, d’un processus. Commencement, début. À l’entrée de l’hiver. Dès l’entrée du repas. Par métonymie. Mets qui vient après les hors-d’œuvre et précède le plat principal. Une entrée chaude, froide. Servir un vol-au-vent, un soufflé en entrée. Par extension. Plat principal. Un repas composé d’un hors-d’œuvre, une entrée et un dessert.
>>>> Par extension. Plat principal. Un repas composé d’un hors-d’œuvre, une entrée et un dessert.
"By extension. Main dish. A meal consisting of an appetizer, an entrée and a dessert."
There the "entrée" is clearly the "main dish".