Poëme is an older spelling of poème, but in poetry studies it can also refer to Alfred de Vigny's idea of a poem that treats a serious philosophical subject in an elevated, often dramatic way. In that sense, it points to a broad, reflective poem rather than a short lyric.
Because the term is uncommon and tied to a specific literary context, it is best understood as a specialized label rather than a standard modern genre name.
Example
Night asked the cliff, "Why stand you here?"
The cliff answered, "To learn endurance.
The sea asked again, and the silence
held its thought like a stone in the dark.