Suicide in the Eiffel Tower is apparently quite common. France has one of the highest suicide rates at 17.5 suicides per 1000 people! Killing yourself with the 1,063 foot “Iron Lady” is the third most popular French suicide method behind poisoning and hanging.
A few times, people have attempted to kill themselves but failed to do so. It's reported that one man was blown onto a rafter by the wind and he was spared. The most curious case is one of a woman who jumped, landed on the roof of a car and later married the man who owned it!
In an effort to reduce the number of suicides off of the Tower, six foot tall barriers were built around the tower. It has worked very well as the suicide rates have gone down exponentially. However, 4-5 cases of suicides a year in the famous city still happen.