Made inroads in French, taught to handle grammar, finally (10)

'made inroads' is the definition.

'in french taught to handle grammar finally' is the wordplay.
'in french' becomes 'en' ('en' can be French for 'in' e.g. en France).
'taught' becomes 'coached' (coaching is a kind of teaching).
'to handle' means one lot of letters goes inside another (handle can mean receive or take possession of).
'finally' says to take the final letters.
The last letter of 'grammar' is 'r'.
'coached' enclosing 'r' is 'croached'.
'en'+'croached'='ENCROACHED'