I’m a native French speaker, and “charcuterie” doesn’t really carry that negative meaning in everyday use. It’s very commonly used to mean cold cuts / prepared meats.
The butcher is un charcutier, and the shop is une boucherie. La charcuterie refers to the food itself, usually cured or prepared meats (pork, cooked, smoked, dried, etc.). So the name works the same way it does in English.
I'm French too :-)
I get why people use French words to name products in english, but une charcuterie, it's somewhat gross and messy. It's Gaulois in a sense. To me it clashes a lot with the look of the website which is more like Tron-ish.
You wouldn't see a charcutier in Tron, would you?