The French studies could produce languor (9)
I believe the answer is:
lassitude
'languor' is the definition.
(I know that languor can be written as lassitude)
'the french studies could produce' is the wordplay.
'the french' becomes 'la' ('the' in French).
'could produce' indicates anagramming the letters (I've seen this in other clues).
'studies' anagrammed gives 'ssitude'.
'la'+'ssitude'='LASSITUDE'
(Other definitions for lassitude that I've seen before include "slackness" , "Listlessness, fatigue" , "Is saluted with tiredness" , "30 [LETHARGY]" , "Listlessness, state of apathy" .)