It's certainly not a free market. Cities commonly provide exclusive franchise to specific companies. I've got Cox internet and access to Cox cable. AT&T provides phone service, but not any kind of internet access. My access options are Cox, mobile, or satellite. Mobile and satellite obviously have much smaller max transfers per month; they wouldn't cover my requirements for household internet.
Capitalism simply means the government doesn't own the infrastructure and provide the service to use that infra. It is not free market in terms of it being a competitive market. It is a free market if you think "free" means unregulated (or less regulated).
But it's a shift of the goal post to consider free markets as unregulated ones. It was for a long time well understood that good regulation ensures competitive markets. Or when there can be no competition, to have highly regulated monopolies to in effect legislate the outcome that most people who are politically active want.