「」。
The moment she said "I wanted to see you," she burst into tears.
Literal
She [topic-は] "meet-want-to-was [feminine-わ]" [quotative-と] say [as-soon-as-なり] cry-burst-out [regret-てしまう] did.
~なり is a literary conjunction meaning 'as soon as, the moment that' — attaches to the dictionary form of a verb and marks immediate succession. お会いしたい uses the humble お+masu-stem+する pattern (お+会い+したい), elevating the speaker's own act of meeting toward the listener. The sentence-final わ is the soft feminine ending, marking gentle assertion. 泣き出す ('burst into tears') is a compound verb 泣き + 出す, with 出す as the auxiliary for sudden onset. The whole sentence is filmic — restrained dialogue followed by sudden tears.