Great question — answering as the UphillTech team:
Egg replacements are an option depending on where you live and what products are available, but from what I hear they don't produce a similar result to eggs. Most egg-free french toast recipes use applesauce mixed with milk or yogurt and a bit of sugar for dipping, and from what I've heard they work well.
Full answer by GdD: https://cooking.stackexchange.com/a/63240 (CC BY-SA 3.0).
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