。
She departed for Paris at the end of last month.
Literal
She [topic-は] last-month [possessive-の] end [at-に] Paris [for-に] departed.
先月の終わりに uses に to mark the time point: 'at the end of last month.' パリに出発した means 'departed for Paris,' where に marks the destination. The sentence has two に particles with different functions — the first is temporal (when), the second is directional (where to). This kind of multi-role particle use is common and worth recognizing when parsing longer sentences.