Franklin has worked in the building society sector for 42 years and was a board member of the Coventry from 2008.
Chris White, chief executive of Hinckley & Rugby, said: “He has accumulated vast experience in financial services over the many years he helped lead the UK’s third largest society.
“His achievements are recognised throughout the building society sector. He has a strong track record in corporate governance and risk, plus broad knowledge of working with the regulators. We are very pleased to welcome him to the board.”