Frenchman looking up good quote about lively... (9)
I believe the answer is:
energetic
'lively' is the definition.
(similar in meaning)
'frenchman looking up good quote about' is the wordplay.
'frenchman' becomes 'rene' (common French name).
'looking up' says the letters should be written backwards (in a down clue, letters go up).
'good' becomes 'g' (abbreviation).
'quote' becomes 'cite' (synonyms).
'about' says the letters should be written in reverse.
'rene' backwards is 'ener'.
'cite' reversed gives 'etic'.
'ener'+'g'+'etic'='ENERGETIC'
(Other definitions for energetic that I've seen before include "Lively, dynamic" , "Showing great activity" , "Very active" , "It's vital" , "Forceful and with great vitality" .)