Cant see a Marriage for Francis to Mary at least in Harwich or Essex on FreeREG
You probably have this but Francis/Mary Bapt there;
FRANCIS 05 Apr 1702
JOHN 15 Mar 1705/6, buried 18 Jun 1706
Just posting what I have found in case you don't have it all.
Looks to me that FRANCIS Snr was buried 06 Feb 1705/6
The reason is on the Burial of Son John, Mother is a Widow.
Marriage St Andrew, Greenstead, Essex
13 Aug 1710
Mary PULHAM, Widow** of Harwich to William JEFFERIES of Harwich
Marriage St Mary, Woodbridge, Suffolk
21 Feb 1725/26
Francis PULHAM of Harwich* to Susanna SKINNER