So I'm wondering if the English term "Fridge" for a refrigerator, also derived from the brand of Frigidaire?
I believe it is the opposite. In French, it is common to say Frigidaire when talking about any refrigerator, regardless of the brand. Doing so is technically improper unless the brand is really Frigidaire, but it is widely used. It is the same as saying Electrolux instead of vacuum cleaner, or Kleenex instead of paper tissue.
The word fridge comes from the Latin 'refrigeratio' which means to lower the temperature, to chill. That word is way older than the brand name.