Both elements of the locution hache de nethe are of uncertain derivation, and a corruption of hakeney seems the best explanation. The second element may have been influenced by Middle English net n.2 which includes the locution hed of net meaning 'a single beast'.
s.
hache de nethe
1horseszool.(corruption of ?) hackney, small saddle-horse:
(
1291-92
)
une jumente pris de .vij., souz e une hache de nethe pris de .xij. deners qe il bayla en garde
24
hache2 (1291-92)