Learn French: Nous jouons au basket au stade. - We play basketball at the stadium.

In French, the verb jouer (to play) requires the preposition à when referring to sports and games. Because basket is a masculine noun, à and the article le combine to form the contraction au.

Would the preposition change if we were playing a musical instrument instead of a sport?

Yes! While you use jouer à for sports and board games, you must use jouer de for musical instruments. If you were playing the piano, it would be Nous jouons du piano because de and le contract into du.

Is it a coincidence that au appears twice in this sentence for two different reasons?

Exactly. The first au is grammatically required by the verb jouer for a sport. The second au is a standard preposition of location meaning "at the", where à and the masculine noun le stade contract into au stade.

Is basket the complete word for the sport in French?