After the assassination of Henry IV in 1610 Marie de Medicis decided that as Regent she deserved a better type of palace. Styled after Marie's ancestral home in Florence (the Palazzo Pitti) building started in 1615 and lasted 30 years.
The southern facade of the Palais du Luxembourg
It has been extensively and frequently remodelled since then. It is now the home of the French Senate, and sits in the extensive (23 hectare, or 56 acre) Jardin du Luxembourg. The garden is lovely, and contains many statues (including the 20 notable ladies), playgrounds, a marionette theatre, restaurants and kiosks, tennis courts, basketball courts, and an art gallery. It also has "chalets de nécessité" - their term, not mine.
We visited the garden in September this year, and can thoroughly recommend it as something to do in Paris. The official site is here.