Learn French: Nous faisons du sport dans le parc.

No, faisons comes from the highly irregular verb faire (to do / to make). For nous (we), the ending is -ons just like regular verbs, but the stem changes to fais-. So, we do or we make is always nous faisons.

Why does this sentence use faisons to mean play?

In French, the verb faire (to do / to make) is used with general physical activities. While you use jouer (to play) for specific team sports or games with a ball (like jouer au tennis), you use faire for general exercise. Therefore, to play sports in general is always expressed as faire du sport.

Why is there a du in front of sport?

French requires an article before almost every noun. Because you are doing an unspecified amount of physical activity, it uses the partitive article du, which means some. It is formed by blending de and le. So you are literally saying we are doing some sport.

The English translation says sports, so why isn't the French word plural?

In English, we often use the plural sports to talk about athletic activities in general. In French, the overall concept of exercising is singular: le sport. Using the plural des sports would mean you are talking about several specific distinct types of sports, not just exercising in general.