The free market has never been used to address global warming (it's badly used in general in fact, possibly in part because few people seem to actually understand what it is or even internalize that it's a tool at all, not an end, and like any tool there are applications it is a poor fit for). Amongst the foundational requirements for a free market to work at all is that the price should embody all costs. There are some problems of course where this simply isn't very practical, particularly ones that are heavily non-linear/non-reversible. But that's not the case for carbon emissions, in fact it's a pretty good fit. The problem is "release of fossil/long term stored carbon into the atmosphere", it's easy to measure at various points at the fuel level, and since it's a gas that will evenly diffuse worldwide and is uniform removal from the atmosphere can take place anywhere in the world by anyone using any method. That makes it well suited to abstraction, with a market system on each side of the equation and government acting as a pivot. Wouldn't even require global buy-in to make a difference given that the energy market is primarily globalized anyway, if a few major polities decided to require it and also made access to their own markets take it into account it'd have a major effect no matter what anyone else wanted.

We need to price in the externality. A carbon tax is one way to do that. Instead, we have various direct approaches—fuel efficiency standards, subsidies...—that work with varying degrees of success.

The free market cannot suitably address the "tragedy of the commons".

If all companies currently follow expensive but environment-friendly processes, a rouge company can undercut them by following a cheaper but environment-harmful process. This will either force other companies to follow the rogue company, or they go out of business.

The US Government subsidizes our oil addiction. If the costs were apparent at the gas tank, a “free market” would correct in a blink.