The next morning, when I woke up, I saw fruit tree blossoms blooming under my window.
Literal
Next-morning, eye [subject-が] awakens-[when-と], my [possessive-の] window [possessive-の] below [at-で] fruit tree [possessive-の] flowers [subject-が] are-blooming [nominalizer-の-object-を] eye [to-に] put-did.
目がさめる ('eyes wake up') is the standard Japanese way to say 'to wake up,' with the eyes as the subject — a characteristic agentless/body-part-focused framing. 目にする (literally 'put to the eye') is an idiom for 'see / lay eyes on,' more literary than 見る. 果実 ('fruit') + 木 ('tree') = 'fruit tree.'