Pelota basque is not usually seen listed as an Olympic event in 1900, although Lennartz/Teutenberg did include it in their book. However, it meets all the criteria for inclusion on the Olympic program – amateurs, international competitors, and no restriction of entry.
There were two events contested, one for amateurs and one for professionals. Only the amateur event should be considered the Olympic competition. A third event was scheduled, and this was also for amateurs and would have been an Olympic event as well, except that there were no entrants. The third event was paume à main nués – game of the open palm, which sounds suspiciously like the American version of handball.