Château de Vincennes
(panoramic view taken from the keep, showing almost 180% of the site)
This massive, grim fortress, currently under restoration, dates back to the 12th century. It retains many of its impressive medieval towers, and was kings' residence for several centuries. It was here that Henry V (victor of the battle of Agincourt) died.
(It is barely mentioned in Paris - it is just outside the Paris city limits, whereas the spacious large Bois de Vincennes is within Paris - but is well worth a visit. Just go to line 1 of the Paris metro and travel eastwards to its terminal.)