Regular coke is about as vegan as regular pickles.
Pretty terrible analogy. I have no idea if pickles are vegan or not. I would assume they are but I'm not steeped in the vegan ethos and many things have surprised me in the past as being non-vegan.
Animal products are constantly snuck into processed, preserved and packaged foods. I'd find it funny, but wouldn't be surprised, to find that something derived from an animal found its way into a jar of pickles 'for flavor'.
Interestingly, if it's 'throwback' coke with white/processed sugar in it, it's NOT vegan, as animal products (mostly bone/etc.) are used in the production of that sugar.
HFCS modern coke is generally considered vegan.
Vegan french fries is the stand out here. Many commercially available ones are flavored and/or cooked with non-vegan ingredients.