The French department giving a few extra marks (5)
I believe the answer is:
somme
'the french department' is the definition.
(administrative region or department of France)
'a few extra marks' is the wordplay.
I cannot really understand how this works, but
'marks' could be 'm' (former German currency) and 'm' is located in the answer.
'few' could be 'some' (associated in meaning) and 'some' is located in the leftover letters.
No letters remain.
This may be the basis of clue (or it may be nonsense).
'giving' acts as a link.
Can you help me to learn more?
(Other definitions for somme that I've seen before include "WW1 battle site" , "runner" , "French river; WW1 battle" , "French river known from First World War" , "bloody fight" .)