In club play or friendly neighborhood play, teams often play several games in a row.
In English, we would say that after the “match” comes the “rematch” or “return match”. In petanque, in French, after the first game, the loser may propose la revanche.
If after two games the teams are tied (one game to one game), the teams may decide to play a third “playoff” game, la belle (the beauty).
I don’t know the origin of the term. In French belle means beautiful, but the expressions de belle and de plus belle mean (roughly) “even more” or “more than ever”.
In any event, the terminology lends itself to petanque humor — gently risqué double entendre.
— “You won (gagné) the first game (la première). We won the second (la seconde). Shall we do the beauty (la belle)?”
— “OK,” he says (throwing away his boule and heading toward his mixed-doubles partner, a very attractive young woman). “I’ll go first.”