Name grand Frenchman on the rise that's very active (9)
I believe the answer is:
energetic
'very active' is the definition.
(I've seen this before)
'name grand frenchman on the rise' is the wordplay.
'name' becomes 'cite' (I've seen this in other clues**).
'grand' becomes 'g' ('G' can be a synonym of 'grand').
'frenchman' becomes 'rene'.
'on the rise' is a reversal indicator.
'cite'+'g'+'rene'='citegrene'
'citegrene' reversed gives 'ENERGETIC'.
'that's' is the link.
(Other definitions for energetic that I've seen before include "Vigorous and dynamic" , "Showing great activity" , "It's vital" , "Full of go" , "High-powered" .)