Agincourt by Bernard Cornwell

Agincourt: A Novel - Nicholas Hook is a forester in England during King Henry V.  Because he hit a priest, he faces hanging.  Given advice on how to escape, he is employed by a lord who is building forces to aid the English forces in France to recover the French crown for the English king.  The story follows Hook's from England to France for the battles at Harfleur and Agincourt.

Although this is not a part of The Grail Quest series, Thomas Hookton is mentioned in passing.