The gothic church without towers just below the Sacré Cœur in the photo is Saint Eustache at les Halles. The gothic spire on the left, just behind the pointy green roof, is the Sainte Chapelle on the Ile de la Cité.
I won't go into the details of why it was built -- lots of guilt, remorse, political, religious and moral stuff, all of which you can look up on the internet if you're interested. But since it was built, up on the heights of Montmartre, it has become an icon of Paris and a tourist mecca. The views out over the city from the terraces are terrific. I have yet to climb up into the church's dome. Maybe one day!