It's so funny as a French person to see this x) Here we learn it in primary school, but now… time for me to practice my English!
In 1889 Paris hosted the World's Fair, which gathers the best inventions and art pieces from many countries. Each country had to build a structure to expose their treasures. So Gustave Eiffel from France build the highest tower of his time to prove his country was the best (obviously, because French people are modest you know). It was made of iron and painted in red. After the end of the Fair, Paris decided to keep their pavilion up instead of dismantle it, and open it to the public. That's how a temporary structure became the most internationally known monument of our country.
Now it's not red anymore, it's iron coloured with a lot of lights so it brightens in the dark for the whole night.