In my opinion, there's far too much focus on French terms for culinary practices — TODO.
Some innovations that were clearly novel:
The system of hierarchy within a professional kitchen[2]. This isn't the only way to manage a large kitchen, but 1) it's definitely a valid way, 2) it was novel when it was developed in France, and 3) many other countries have adopted it.
Things that some cooks try to portray as the sole innovation of French cooking, but that almost certainly existed in other countries around the same time, and may have predated the French innovations of the 19th century:
Mise en place — Just call it ingredient gathering, my god. I haven't found hard evidence that it was used outside of French cooking before this (I haven't looked), but it feels (that's an assumption there, I fully admit) like this is likely not unique to French cooking at the time.
Mother sauces — Too many people in forums interpret mother to mean "these are the most important sauces" or even "the only important sauces". This is clearly a misinterpretation, since French cooking talks about mother sauces and daughter sauces. However, it still feels like this term is one of the ways that Eurocentrism in culinary discussions is propagated. Personally, I prefer to put the emphasis on "these are the core sauces that are important to the French system", since there many other important sauces from around the world.
Beurre monté — Just call it a water/butter emulsion. Again, I'm assuming (I haven't searched) that this existed before / outside French cooking at the time, since it seems like such a simple concept.