I can't speak for telcos, but I'll try to answer on behalf of the cable TV industry, which now offers telephone service.
In all states, US cable TV companies are usually required to pay franchise fees based on revenue derived from the provision of video services and certain services incidental to the provision of video services (e.g., equipment rental, ad commissions); however, they are exempt from paying franchise fees on revenue derived from the provision of internet access ("cable modem") service or telephone service. These fees constitute payment for the right to place facilities on public (locally-owned) rights-of-way. Franchise fees are assessed by local franchising authorities (LFAs).
In most jurisdictions, cable TV companies are required to pay property taxes on owned real estate (land and buildings). These are taxes of general applicability, unrelated to the provision of cable TV service; they are based solely on the assessed valuation of the property.
Cable systems owned by non-profit corporations are generally exempt from taxes. They may or may not be exempt from franchise fees, depending on the language in the franchise document itself.
Cable systems owned by government agencies are generally exempt from all taxes and fees.
Neal McLain