The key difference is the number of slots. The European and French roulettes have 37 slots, including 36 numbers and one "zero". The American roulette wheel has an additional "zero" slot (00), and that results in an increased total number of slots (38 in total). This peculiarity interferes with the house edge. You will give 2.70% for playing European or French roulette, and 5.26% for playing American roulette. There are rules which can reduce the house edge to 1.35%.