Riddle in French initially intriguing key family member (6)
I believe the answer is:
enigma
'riddle' is the definition.
(I know that riddle can be written as enigma)
'in french initially intriguing key family member' is the wordplay.
'in french' becomes 'en' (French word for 'in').
'initially' says to take the initial letters.
'key' becomes 'g' (musical key).
'family member' becomes 'ma' (ma can informally mean someone's mother).
The first letter of 'intriguing' is 'i'.
'en'+'i'+'g'+'ma'='ENIGMA'
(Other definitions for enigma that I've seen before include "Coding device" , "Mysterious person/thing" , "Mysterious person" , "Mysterious puzzle" , "WW2 code" .)