To veganize - instead of the eggs, puree 6 oz silken tofu with 2 Tbsp non-dairy milk, OR for a more flavor-packed option, stir together 2 Tbsp dijon mustard, 2 Tbsp maple syrup, 1 Tbsp soy sauce and 1 Tbsp Vegenaise.
If you don't have a wire rack to bake the fries on, it is completely fine to bake them on parchment paper or greased aluminum foil - just turn them halfway through baking.