I was only in Madrid two days, three nights. For me, the must-sees are a bullfight at Las Ventas Stadium, the Prado Museum (half-day minimum), La Reina Sofia (half-day minimum), and a walking tour of the city (one or two days). Rick has several suggested walks for Madrid in his guide book and points out what you're seeing. Maybe schedule a food tour? Though I like to eat when I travel, I'm not a foodie, yet, in Madrid, I noticed how good the food is. Rick will have suggestions in his guidebook.
I would recommend against flying to Paris and then flying back to Madrid to catch a flight home unless you're dead set on it. It's nothing against Paris, as I've visited the City of Light three times. The reason is you'll lose a half-day going there and a half-day going back. Why not stay in Spain? A superb second choice to visit is to go to Sevilla. Another good idea is to visit Toledo, the ancient capital of Spain.