The French girl oddly lacking a name (5)
I believe the answer is:
leila
'name' is the definition.
'the french girl oddly lacking a' is the wordplay.
'the french' becomes 'le'.
'oddly lacking' means one should take alternating letters.
The alternate letters of 'girl' are 'il'.
'le'+'il'+'a'='LEILA'
(Other definitions for leila that I've seen before include "Girl" , "Eric Clapton song" , "Arab woman" .)