Move rapidly, having offended the French (6)
I believe the answer is:
hurtle
'move rapidly' is the definition.
'hurtle' can be an answer for 'move' (hurtling is a kind of moving). I am not certain of the 'rapidly' bit.
'offended the french' is the wordplay.
'offended' becomes 'hurt' (I've seen this before).
'the french' becomes 'le' ('the' in French).
'hurt'+'le'='HURTLE'
'having' is the link.
Can you help me to learn more?
(Other definitions for hurtle that I've seen before include "Proceed quickly and noisily" , "Rush violently" , "Dash, move rapidly" , "Move fast; rhymes with marine reptile" , "Career (along)" .)