I can't spot the James/Katherine marriage either, but maybe push the search date back a bit as they had a son James bpt 1687 Brixworth.
There was in Brixworth another couple who married 1671 - John Cook & Anne Allom. Their children appear to have been Mary bpt 1671, John 1673, Philip & Thomas twins 1675, Thomas 1678, Elizabeth 1680, James 1682, Robert 1686, Francis 1688.
Maybe this Elizabeth is worth looking into.
(Sources: Northants Baptism Index, Northants Marriage Index)