Book that woman's carrying is in French (6)
I believe the answer is:
esther
'book' is the definition.
(book of the Hebrew Bible)
'woman's carrying is in french' is the wordplay.
'woman' becomes 'her' (pronoun for a woman).
'carrying' is a charade indicator (letters next to each other) (in a down clue, the bottom letters carry others).
'is in french' becomes 'est' ('is' in French).
'her' after 'est' is 'ESTHER'.
'that' is the link.
(Other definitions for esther that I've seen before include "Biblical heroine who became queen of Persia" , "Now there's a lady" , "Old Testament queen" , "Old Testament book telling of a beautiful Jewess" , "Beautiful lady" .)