Hi

You may have looked into this but its the only other thing i can think of, if Francis father was a wealthy man he may have left a will. Wiltshire Council have some 50 wills for Fox including Henry Fox Gentleman 1663.
Some of the wills can be purchased on line and sent direct to your computer some you have to order and they are not expensive to buy, there could just be a mention of Francis in the will if only to disinherit him

http://history.wiltshire.gov.uk/heritage/

Shelagh