We visited the Sacre Coeur Basilica on Easter Sunday of 2017. The church is located in the top of the butte Montmartre, which appears to be the highest point in Paris. Fear not, it's not so steep of a hike and besides, you can take a funicular on the way up if you like. So to recap, you can make your way up via streets or take the steep 300 steps hurdle to the top powered by your legs. Alternatively, you can take the Funicular up for the price of a metro ticket (roughly). Which is really not expensive. Unfortunately (or not) we found out about the funicular on the way down. It was really cool and we recommend it for either way, as it displays a really nice view of Paris.
When arriving in Paris, our taxi driver explained that we could get great views of the city from the Sacred Coeur. Which meant that we didn't need to pay for the Eiffel Tower or Arc de Triomphe to see Paris. Consider visiting Sacre Coeur first for free, then make the call if you want to pay for other monuments / landmarks,
The Basilica is really beautiful inside and out. Yes, it’s totally worth to wait in line to visit inside. It's free to enter and you have an option to download a free audio guide if you have internet. We think there is an option to pay a fee to get a panoramic tour, but we went during Easter, it was really busy and we didn’t find how to get there.
According to Wikipedia, the basilica was designed by Paul Abadie and the construction began in 1875. Oddly, it was only completed in 1914, pretty interesting!