They're not cooked in tubs of beef fat, like the old days, or trans-fats like the less-old days, but the latter is because the public (correctly)perceives trans-fats as unhealthy. They still have beef fat in the pre-cooked frozen fries, for flavor purposes, so they're still not edible for us vegetarians, they're just less unhealthy for you carnivores.
Burger King doesn't use meat fat in their fries, and they also have veggie burgers, Five Guys probably makes the best fries, In-n-Out's are ok if you get the right out of the fryer (they're actually made by chopping potatoes, instead of heavily-processed frozen stuff, so they don't last as long, and if you're not vegan you can get animal-style fries, which are a sort of California poutine grease overdose (yay!))