"I am playing tennis."
Translation:Je fais du tennis.
Why is there no verb for play? Can fais be used for make, play, perform, build etc just like this?
There is - jouer = "to play". Remember faire (the infinitive of 1st and 2nd person singular present indicative fais) also means ""to do". And, according to Larousse, it can also mean a few of the things you mentioned:
When referring to an activity, you usually can use the generic verb "faire" or a specific verb related to the activity.
Je joue au football = "Je fais du football"
Je fais de la musique = "Je joue de la musique"
Je fais de la peinture = "Je peins",
and Je joue au tennis = "Je fais du tennis".
Isn't jouer the verb To Play? Although I'm not sure why it wasn't used in this sentence