Much like its cities, like Metropolis, Gotham City and Opal City, which are made up rather than part of the real world, there are many other facets that are fictitious as well like companies, sports teams, and yes, even fast food restaurants.
There's Big Belly Burger, which just made its prime time TV debut in the third episode of "Arrow." There is also O'Shaughnessy's, sort of a Denny's, named after DC Comics writer/editor Denny O'Neil's penname.
There's also Burgie, a major fast food chain. Burgie is a close cousin to real world counterpart McDonald's with its sideways Golden Arches forming a B. One or all of these restaurants probably served Soder Cola. Big Belly Burger appears to be similar to Bob's Big Boy, and is owned by LexCorp, for better or worse.
And nope, sadly I have no idea what kind of fries they serve...
