No. If you were saying something like The Sacramento Ballet, which has a very good production of the Nutcracker, it would be capitalized. I hope I helped and go see the Nutcracker in Sacramento, it is really, really, really good.
Is Ballet A Proper Noun?
I don't believe that ballet is a proper now. Think of it like this. A noun is a person place or thing. And ballet is none of those. And a proper noun is like the name of a city, or person, and item ect. And ballet is just the name of a dance so I don't believe that it is proper.