Built in 1875, the Palais Garnier is a gem. It's very worth taking the tour if you cannot get tickets to a performance. It was the sole opera house before the Opera Bastille was built in 1989. Now it mainly has ballet performances; however, we were able to catch an opera here on our trip, and what a beautiful setting it was.
The season tickets had been sold out since the summer; however, it is possible to get last-minute tickets by going to the box office on the same day. Instead of purchasing the 130€ seats that were left, we stood in the line that was forming outside the box office and found that right before the performance, seats would be sold at deep discount rates. After waiting in line for 1 1/2 hours, we got tickets for 7€ each; unfortunately, these were seats that had a very limited view of the stage. They were so high up, we could touch the ceiling! The music was beautiful (it was a performance of Mozart's "Don Giovanni" cleverly staged in a modern-day setting that really worked for the story), so even though we could only see one corner of the stage, it was still very worth it to be in the theatre and hear such a fantastic opera.
The opera building itself was incredibly ornate: gilded carvings, columns and statues, various kinds of colored marble in the grand foyer, and a gorgeous ceiling fresco that was repainted by Marc Chagall in 1964, featuring figures from famous operas.