"He meets her and falls."
Translation:Li renkontas ŝin kaj falas.
Be carefull with the figuratively fallings.
"Fali" = "come down thanks to grabity".
"Fall in love" is an English expresion, in other languages no one "comes down" in love. So, in Esperanto that English point of view is not used.
fall in love = en'am'igxi
love (someone) = am'i
lover = am'anto