The Opera Garnier made this list because Vincent takes Kate there to watch the ballet. And classical ballet as we know it today actually originated from the Opera Garnier. Though the naming can get confusing.
The Opera Garnier is the company that was founded in Paris in 1669. Between 1861-75 the Palais Garnier, named after its architect, was built. It was the primary home of the Paris Opera, which therefore became known as the Opera Garnier. In 1989 the Opera Bastille opened. The bigger and modern building of the Opera Bastille is now the primary building of the Paris Opera, while the smaller, abundantly decorated Palais Garnier is mainly used today for ballet and classical opera productions. But the Opera Garnier is still the more famous building, not last because the Phantom of the Opera lives there.