Where, in France, cave men lost heart (4)

I believe the answer is:
caen
'where' is the definition.
The definition suggests a singular noun which matches the answer.
'france cave men lost heart' is the wordplay.
'france cave' becomes 'ca' (I can't explain this - if you can you should believe this answer much more).
'men' becomes 'enlisted men' (enlisted man is a kind of man).
'lost heart' says to hollow out the word (remove centre letters).
'enlistedmen' with its middle removed is 'en'.
'ca'+'en'='CAEN'
'in' is the link.
Can you help me to learn more?
(Other definitions for caen that I've seen before include "French city" , "City in Normandy" .)