North Sea region the French backed? Nonsense (8)
I believe the answer is:
'nonsense' is the definition.
(I've seen this before)
'north sea region the french backed?' is the wordplay.
'north sea region' becomes 'dogger' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'the french' becomes 'le' ('the' in French).
'backed?' says the letters should be written backwards.
'le' written backwards gives 'el'.
Can you help me to learn more?
(Other definitions for doggerel that I've seen before include "Bad verse - of canine beginnings?" , "Badly written verse" , "Nonsense verse" , "Trite verse" , "Terrible poetry" .)