Marisa C. Hayes

Renowned as a choreographer, director, performer and visual artist, Dimitris Papaioannou wears many hats but is hesitant to label himself.

Throngs of eager spectators have lined the steps of Paris theatres in recent months, while last minute ticket seekers display homemade signs—often in vain—hoping to access sold-out performances.

As Dancing Pina opens, a camera towers over a performer lying face down on a studio floor. Delicately inching her forearm along the ground, the dancer is scrutinized by Malou Airaudo, who intervenes with agitated intensity.

How do dancers in the world of classical ballet obtain a promotion? The question is rarely asked because most often it is assumed that a dancer’s rank is determined by a company’s Artistic Director. Not so at the Paris Opera Ballet...