Consumer Access to Broadband for Local Economies and Competition Act or the CABLE Competition Act This bill modifies the process for transferring a cable franchise to a person to whom such franchise was not initially granted. Specifically, the bill prohibits a cable franchising authority from (1) precluding the transfer of a cable franchise from a cable operator to a person to whom such franchise was not initially granted, or (2) requiring a cable operator that was initially granted a franchise to receive approval from the franchising authority for such a transfer. However, a franchising authority is authorized to require a cable operator to notify the authority of such a transfer.