Hytner quit as the bank's group brand and UK banking marketing director in August to move to Top Up TV as commercial director.
Barclays' reshuffle means there is no group brand director role any longer, although marketing directors from the various business divisions will sit on a brand reputation committee.
Jeppeson has been promoted from direct response marketing director just five months after joining Barclays from Capital One.
He will report to Deanna Oppenheimer, the UK banking group's chief operating officer.
French, who was formerly head of group customer service, will take responsibility for marketing the business banking division, Barclays Commercial Banking.
Under Hytner, Barclays had invested in a BBH-created advertising campaign that aimed to give the bank a more human face by using employees coming up with ideas for new services.