The French framing a note in error (5)
I believe the answer is:
lapse
'error' is the definition.
(lapse is a kind of error)
'the french framing a note' is the wordplay.
'the french' becomes 'le'.
'framing' means one lot of letters goes inside another.
'note' becomes 'ps' (PS is an example**).
'a'+'ps'='aps'
'le' placed around 'aps' is 'LAPSE'.
'in' is the link.
(Other definitions for lapse that I've seen before include "A slight error or a passage of time" , "Decline into an inferior state" , "Error; oversight" , "Momentary mistake" , "Go back to bad behaviour" .)