One French son lost interest in Henry being trained (10)
I believe the answer is:
unschooled
'one french son lost interest' is the definition.
I can't tell whether this definition defines the answer.
'henry being trained' is the wordplay.
'henry' becomes 'un' (I am not sure about this - if you are sure you should believe this answer much more).
'being trained' becomes 'schooled' (I've seen this in another clue).
'un'+'schooled'='UNSCHOOLED'
'in' acts as a link.
Can you help me to learn more?
(Another definition for unschooled that I've seen is " Lacking formal education".)