The Chateau was The Merovingian's mansion, located in the Mountains, a remote moutainous area resembling the Alps. Neo has to fly about "500 miles due south" to save Morpheus and the Keymaker in Mega City.
The Keymaker was imprisoned there by The Merovingian. After making a deal with Persephone, she led Neo, Trinity and Morpheus to the mansion to retrieve The Keymaker. Then, she killed Abel and told Cain to go and notify the Merovingian.
When The Keymaker was freed, The Merovingian showed up. The Twins went after The Keymaker who ran away followed by Morpheus and Trinity and made their way to the Chateau's garage. Meanwhile Neo easily fought, and defeated The Merovingian's henchmen.
When the fight ended, the Merovingian left and closed the door of the Chateau. Neo opened it and found himself in the Mountains. After Morpheus and Trinity left with a car, Neo looked for another exit. Neo saw a Twin who grinned and closed the door between them. Neo smashed it and again ended up in the Mountains.
He decided to fly away and made it just in time to save Morpheus and The Keymaker during the pursuit.