Consumer Access to Broadband for Local Economies and Competition Act or the CABLE Competition Act This bill limits the authority of state and local entities that regulate certain aspects of cable operators (franchising authorities) over the sale or transfer of franchises for cable systems. Under current law, cable operators must typically obtain franchises authorizing them to provide services in a given area, and franchising authorities may place conditions on sales or transfers of franchises for cable systems. Under the bill, franchising authorities may neither (1) prohibit a cable operator from transferring its franchise to another operator, nor (2) require an operator to obtain approval when transferring its franchise to another operator that accepts all of the franchise terms. However, a franchising authority may require a cable operator to notify it of a transfer.