Human rights are fundamentally different from environmental policy in an important way.
To keep the environment well, you need to have all countries on board. If one big industrial country doesn't go on board, then it will have an advantage. That country can make products cheaper and may even attract companies because of it.
Furthermore, if many large companies just move to those countries, the net effect on the environment is nonexistent (at least for those emissions) except the countries that do take part lose business. Indeed, whether I pollute the air in Germany or in France doesn't matter much, we all share the same air (and other things to some degree as well).
Rights applying to individuals are fundamentally different. If Germany treats its citizens well with lots of protections then that's good for them regardless of what other countries do. Germany doesn't lose out as much (assuming the rights are pretty basic and not a big burden on business or citizens).
In particular, the rights that Germany guarantees directly benefits its own citizens. Therefore, Germany (or rather its population, which goes hand in hand because it's a democracy) has a good incentive for setting basic human rights just for that reason.
What is similar
Of course, in both cases it's best to work together as countries, as in a scenario where everyone works together the total gain is the highest.
In game theory, these can be seen as Nash equilibria. Let's say (very simplified) that every country can either choose to participate for the common good or not. Then there is such an equilibrium if and only if there is no country that gets in a better position by unilaterally changing its choice regardless of the others.
In case of human rights, countries that value them can participate without losing anything significant (again, roughly, in reality there may be more considerations). Countries that don't value them simply don't participate and don't lose much either.
In case of the environment, there are important reasons not to participate. Indeed, by not participating their businesses can make more profit. I think most of the reasons for not participating (or not being as ambitious as one might want to be / is needed) and they are mostly economical for the benefit of those countries.
Dr Peter John Wood of the Australian National University has some nice slides on climate change participation from a game theory perspective. If you search, especially using Google Scholar, I'm sure you can find more examples of game theory applied to international cooperation, both on the environment and more local issues like human rights or otherwise local cooperation.