Not turning back after getting close to the French city (7)
I believe the answer is:
preston
'city' is the definition.
(city in Lancashire)
'not turning back after getting close to the french' is the wordplay.
'turning back' says the letters should be written backwards.
'after' means one lot of letters go next to another.
'getting' indicates putting letters inside.
'close to' indicates one should take the final letters (the close of something is the end).
'french' becomes 'prs' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The last letter of 'the' is 'e'.
'not' backwards is 'ton'.
'e' placed within 'prs' is 'pres'.
'ton' put after 'pres' is 'PRESTON'.
Can you help me to learn more?
(Other definitions for preston that I've seen before include "English city" , "Town on the Ribble" , "Administrative centre of Lancashire" , "city (as of 2002)" , "Town in Lancashire" .)