Counting from the ground, there are 347 steps to the first level, 674 steps to the second level, and 1710 steps to the small platform on the top of the tower. The public can only climb as far as the second level via the stairways. Public access to the summit is by elevator only.
But...have just found this on Wikipedia...
According to the official website for the tower, the summit is reached by 1,665 steps and not, as popularly believed, by 1,792 steps (the same as the year of the First French Republic).