Competent expertise is short at French university (7)
I believe the answer is:
skilful
'competent' is the definition.
('skilful' can be a synonym of 'competent')
'expertise is short at french university' is the wordplay.
'expertise' becomes 'skill' (I've seen this before).
'is short' means to remove the last letter.
'at' is a charade indicator (letters next to each other).
'french university' becomes 'ful' (I am not sure about this - if you are sure you should believe this answer much more).
'skill' with its last letter taken away is 'skil'.
'skil'+'ful'='SKILFUL'
Can you help me to learn more?
(Other definitions for skilful that I've seen before include "7 [CLEVER]" , "Adroit" , "Deft" , "exhibiting crafts" , "Very adept and proficient" .)