The Petit Palais (Small Palace), like the Grand Palais just across the street, was built for the Universal Exhibition of 1900. Since 1902, the Petit Palais has been the home of the Fine Arts Museum of the City of Paris. The building was thoroughly and elaborately renovated from 2001 to 2005.
Various art collectors have donated or bequeathed their collections to the museum, so it has numerous and varied works of art on display, from all periods up to the First World War.
As in most of the other city-owned museums in Paris, admission to the permanent collection of the Petit Palais is free. The museum is closed on Mondays but is open on Tuesdays, when most of the big state museums are closed.
Thanks to lexandneek for pointing out that the sculpture in this photo (in front of the Doré painting) is called “The first funeral” and was made by Louis Ernest Barrias, dated 1883.
Other museums owned by the City of Paris include the house of Balzac, the Musée Carnavalet (museum of the history of Paris), the Musée Cognacq-Jay (museum of the eighteenth century), the Musée de la vie romantique, the sculpture museums of Bourdelle and Zadkine and the former apartment of Victor Hugo at Place des Vosges.
My photos in this post are from 2012. I revised the text in 2018.
See also: Petit Palais Museum in Avignon.