Not fluently.
Spanish is her native language.
English is spoken fluently (thanks to her parents' choice for the English-speaking Northlands College in Buenos Aires).
Dutch is spoken fluently (with a strong accent and grammatical errors)
French is spoken at conversational level.
German is spoken at conversational level (thanks to the German relatives and the annual holidays in Austria).
Here you see and hear Queen Máxima receiving the French President, in French, at the Petit-Palais in Paris for their "counter-event" in the framework of their State Visit to France (conversation at 0.50):