。
She went to Paris to study ballet.
Literal
She [topic-は] ballet [object-を] learn [purpose-ために] Paris [to-へ] went.
バレー is technically the spelling for volleyball (バレーボール), while バレエ is the standard spelling for ballet (from French ballet). In casual writing the two can blur, and the surrounding context — going to Paris to learn it — pins this firmly to ballet. Paris has been the spiritual home of classical ballet since the 17th century, so traveling there for serious study is a real and well-trodden path. ~ために expresses purpose: 'in order to do X.' へ marks direction of motion, slightly more formal than に for the same role.