Anime is such a specific use, and this is disappointing for anyone with that use in mind. Naming things is hard I guess????
if I said Anime, would you think Tiny Toons, Family Guy, Toy Story, or Lion King? Or would you think DBZ, Akira, One Piece, etc?
It's really interesting how much lore we've created in our forums that doesn't actually exist in the country of origin.
'Anime' in English means cartoon that is at least partially originates from Japan. Or, a less common usage is cartoon that has the style of the former cartoons (e.g. Avatar). 'Anime' in Japanese or in French can mean different things.
We're talking French and Japanese here so let's look at one going the opposite way - the french avec to アベック/ abekku. In French it just means 'with' - eggs with ham, let's go to the beach with friends, whatever. In Japanese it is used to mean that you're romantically with someone, and is used as a noun to stand in for the word couple.
Or for a more specific usage example, high ball in English refers to any mixed drink where the base spirit is a lower volume of the drink than the mixer, e.g. gin and tonic, screwdriver, etc. In Japan a ハイボール / hai barru refers almost universally to whiskey and soda water. Of course other highball drinks are served there, but will tend to get a more specific name, such as a shochu highball being a チューハイ / chuhai.
It's more rare for this to happen with a chain of original word -> loan word -> loan word, but still something that happens - it's called 'reborrowing' a word. Another example of this would be the Chinese having reborrowed matcha to mean Japanese-style green tea.
It's not silly or wrong to utilize the word anime in the west to refer specifically to Japanese-style animation.