On June 3, 1902 at 9:20 p.m., lightning struck the Eiffel Tower. This is one of the earliest images of lightning striking in an urban setting.
When the Eiffel Tower was built in 1886, it was supposed to last only twenty years before it would be torn down (many in Paris at the time thought it was a terrible eyesore). Wanting his monument to last many years longer than the twenty allocated, Gustave Eiffel credited his tower as a scientific laboratory for meteorological and astronomical observations, physics experiments, an optical telegraph communications point, and a beacon for electric lighting and wind studies. All that, plus the tower’s use as a radio antenna, saved it from demolition.
With regard to lightning in particular, there does not seem to be a large concern about tourist safety from lightning strikes in Paris. The “weather” page on the Eiffel Tower website makes no mention of closing for approaching storms. The tower has been struck a number of times.
As seen in the photo, the tower is equipped with a lightning rod at the top, which moves the energy safely to the ground. And while it might seem that a tall metal structure is the last place someone would want to be during a lightning storm, that metal structure is very similar to a Faraday cage, which actually protects those inside from the lightning.