"I am hitting the ball."
Translation:Je frappe la balle.
Balle: tennis ball, baseball, golf ball, ping pong balls, and musket balls...
Ballon: rugby ball, football, basketball, soccer ball, volleyball...
Boule: billard ball, pétanque ball, ornament ball for a Christmas tree...
"Ballon" is typically for the largest balls played in sports. The distinction between "boule" and "balle" is much murkier.
Ballon: A large ball filled with air and that can easily bounce.
Boule: A heavy and dense ball
Balle: A ball in general.
Note that ballon and boule are both considered balle (making it a generic noun). However, we know for instance that in rugby we use un ballon, so nobody will say balle de rugby, even though technically it is une balle.