Of the over 14,000 vintage color slides donated by Charles W. Cushman to the Indiana University library, this 1960 photo of a cradle at Fontainebleau is the only one with a "children's furniture" tag.
I did some searching, and it looks like crib bumpers, diamond push presents, and those crazy curtain things the Euros like to drape over their the heads of their babies' beds all date at least as far back as Napoleon. If you can believe it, this was the secondary, less magnificent, more low-key cradle for The King of Rome, Napoleon II, who was Napoleon I's first legitimate child, born to his second wife Marie Louise:
Napoleon François Joseph Charles was born March 20,1811 at Tuileries Palace in Paris. The only legitimate son of Napoleon I (1769-1821) he was known as LAiglon, the Eaglet, and had the title King of Rome (1811-1814) conferred on him at his birth. His mother was Marie Louise (1791-1847), daughter of Holy Roman Emperor Francis II (later Emperor of Austria as Francis I.) who belonged to one of the oldest families of Europe, the Habsburgs. She married Napoleon I on April 2, 1810. The French were delighted when it was announced Marie Louise was with child. On March 20th of 1811 the child was born in Tuileries Palace. The people of France awaited the canon fire announcing the event: twenty one shots if a daughter, one hundred one for a son. At the twenty second shot cheers burst out; Napoleon had a son. The child slept in a magnificent cradle produced by the collaboration of Thomire, Odiot, and Prud'hon. A delighted Napoleon gave a 275-carat diamond necklace (shown in the portrait below) to Empress Marie Louise to celebrate the birth of their son. In 1816, after Waterloo Marie Louise left her five year old son in the care of her father, Emperor Francis I, in Austria. She traveled to Italy to take possesion of her Duchies of Parma, Piacenza, and Guastalla, which had been awarded to her at the Congress of Vienna. Marie Louise and her lover Count Adam Adalbert von Neipperg (1775-1829) lived a life of dissipated pleasures at her court in Parma. Napoleon II died of tuberculosis at 21 on August 22, 1832  at Schönbrunn Palace in Austria.
Hmm, looking at all that soft crib bedding in that Gerard painting, The King was lucky he lived long enough to lose his empire, be held captive in Austria, get disinherited of his Duchy of Parma, and die of tuberculosis. Georgian Index has photos of The Cradle, as well as info on the artisans who made it.
 As pointed out below, the date of the KoR's death is incorrect. He died on July 22, 1832, not August 22 1832. Daddy Types regrets quoting the error. Also, LAiglon should prbably have an apostrophe in there somewhere, and lose the cap: i.e., l'Aiglon.