Since the French King Louis XIV was so obsessed with expanding and embellishing his palace at Versailles, you might have thought he spent all his time there.
But no, he had several other Royal Palaces as well, and at least until 1682 he divided his time among them. In her novel L’allée du Roi, Françoise Chandernagor has Madame de Maintenon say this:
“We traveled constantly from one place to another, Saint-Cloud in March, Saint-Germain in April, Versailles in June, Chambord in August, Fontainebleau in September, and each time it was a wonderful sight to see the King move out with his bodyguards, his coaches, his horses, his courtiers, his servants and a multitude people running around him in confusion.” (page 469)

Fontainebleau Palace
Fontainebleau (pronunciation here) was a full-fledged Royal Palace long before Versailles was even thought of. Major construction at Fontainebleau was begun in 1528 during the reign of King François I, who loved the Château particularly as a place to spend time with his mistress the Duchess of Étampes. His son Henri II expanded the château in honor of his own mistress, Diane de Poitiers. The future Queen Consort of Spain, Elisabeth de Valois, was born in the Château of Fontainebleau in 1545.

The main gate of Fontainebleau Palace
According to the Château’s website, “Fontainebleau is the only royal and imperial château to have been continuously inhabited for seven centuries.”
Actually, this is not quite true, because there was an interruption of about fifteen years during the French Revolution (1789-1804). During this time the Château was relieved of its furniture, but the building itself was not damaged. The furniture we can see there now was mostly acquired in the nineteenth century, particularly during the First Empire (1804-1814), when Napoléon I chose Fontainebleau as an Imperial Residence.

Stairway at Fontainebleau Palace (Château)
This horseshoe-shaped stairway, which was first built in the 16th century and then re-built for Louis XIII in the 17th, is something of a trademark of the Fontainebleau Palace. When I was there it looked rather bedraggled and in need of repair.
In January 2015, the French government announced that it was allotting € 115 million for a thorough renovation of the Château of Fontainebleau, to be implemented over a period of twelve years. This will include updating the security system, re-opening Louis VII’s twelfth-century hunting lodge, reorganizing the Château’s collection of 30,000 art works, expanding the Napoléon I Museum and replanting the Grand Parterre, which they say is Europe’s largest formal garden.

The Château from through the trees
My photos in this post are from 2014. I revised the text in 2018.
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That sounds like one impressive renovation plan
One day I really must make the side trip from Paris to here!
Even thus I lived in Versailles, Fontainebleau was from my wife region and first castle she made me visit in France; it has always a sentimental value to me and friend of the castle myself. A lot of history and architecture there! Cheers