I'm not sure if you mean Paris's three main opera companies (the Paris Opéra, the Opéra-Comique, and the Théâtre Lyrique) but the one actually called the "Paris Opéra" dates further back than 1820. Its history officially began in 1671 as the Académie Royale de Musique, housed at the Palais Royal. Over the next few centuries the official name would change several times: the Théâtre des Arts, the Académie Impériale de Musique, back to the Académie Royale de Musique, and finally the Opéra National de Paris. (Those are only the most prominent names--there were several others in between.) The institution has occupied several buildings during its long history (the Théâtre de la Porte-St-Martin, the Théâtre Montansier); the 1820s was one of the milestones in the Opéra's history and location, as you noted, but it was by no means the first. In 1821 the Opéra was housed on the Rue le Peletier, where it stayed until the building burned down in 1873. A new building, the Palais Garnier, was built a few blocks away. This would be the Opéra's official home until the company moved to the Opéra Bastille in the late 1980s. The Palais Garnier still has the old name of the company etched in its exterior, however, and still stages performances of the Opéra on occasion.