"May I have an order of fries, please?" - This would be formal. I have heard "a batch of fries" as well. Formally, we call them "French Fries".
Let's see....think about this...
You say to a friend, "Could I have a french fry, please?" It's just one...so countable. "
"A french fries" is not used...so we would use "fry" instead.
Hope this helps you some. Just some things to know about.
Happy learning!!!