Jeu de paume ("hand-game" or "palm game") was the handball precursor to raquet tennis. Paris' Jeu de Paume Gallery is in an old court.
"Real tennis," or "court tennis" came next. I had fun watching some pros play this on the court at Hampton Court a few years ago. There are a number of Real Tennis courts in the US, including one at the exclusive NY Raquet and Tennis Club on Park Avenue (men only).
Lawn Tennis was invented as a casual outdoor version of the wonderful game. I still prefer playing my tennis indoors: I play much better, and I cannot serve into the sun worth a damn.
Remember the Tennis Court Oath of the French Revolution? I believe that was a Court Tennis court.
Image is Jacques Louis David's Tennis Court Oath. It did not end up well because they were not Americans.