Machine is the product of French and English articles
I believe the answer is:
lathe
'machine' is the definition.
(lathe is a kind of machine)
'english articles' is the wordplay.
'english' becomes 'l' (I am not sure about this - if you are sure you should believe this answer much more).
'articles' becomes 'athe' (two examples of the part-of-speech: a+the).
'l'+'athe'='LATHE'
'is the product of french and' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for lathe that I've seen before include "This is turned out" , "Turning implement" , "Turning tool" , "Wood-shaping machine" , "Turner's machine" .)