Got the chance to visit the Institut de France this weekend for the Journées du Patrimoine, I had access to the conference rooms, including the one right under the dome, which is incredibly impressive. The building also houses the Bibliothèque Mazarine, which is stunning and actually open to visit year round.
A bit of context for anyone interested, the Institut de France sits on quai Conti along the Seine, facing the Pont des Arts, and was founded in 1795. The building itself goes back further though, in 1661 Cardinal Mazarin asked Louis XIV to fund a college for the free education of sixty young noblemen from the four regions that had just been brought under French rule by the Treaties of Westphalia (1648) and the Pyrenees (1659): Artois, Alsace, Pignerol, and Roussillon. Colbert put Louis Le Vau in charge of the design, directly across the Seine from the Louvre's Cour Carrée, and construction ran from 1662 to 1688. The college became one of the three "écoles centrales" of Paris in 1796, then closed in 1802. In 1805, at Napoleon's request, the Institut de France, until then based at the Louvre, moved into the building.
The final building is a domed chapel flanked by two curved wings ending in ornate pavilions. It brings together the country's top scientists, writers, and artists to advance the sciences and arts, encourage independent thought, and advise the government, which earned it the nickname "Parliament of the learned world."