The Netherlands are already planning what to do with rising sea levels during the next hundred years or more. It will be expensive.
Talking about the economics of moving away from fossil fuels, there are different situations and potential mechanisms dealing with the allocation of costs and benefits (this is economics textbook stuff).
1 if the the cost for the end user of sustainable energy is lower than the cost of fossil fuel, market forces will persuade end users to make the change. This is already happening with solar energy and wind energy in many locations. Similarly heat pump technology will soon have a competitive advantage.
2 if fossil fuel remains cheaper in particular applications, we have the free rider problem: individual end users are better off sticking with fossil fuel, but collectively we are better off if everyone makes the change. Within national states the free rider problem is usually dealt with on the one hand with legislation to ban or mandate particular behaviour, or, more flexibly, with taxes and subsidies to change the cost benefit equation for economic subjects. Auctions of pollution permits are another clever one. The precise format is something economists can get very excited about, to find just the most effectve mechanism.
3 if the benefits are only global, we have a problem, because we have no global government, thus allowing individual countries to be free riders: why would country X incur substantial costs if the benefits are not felt in that country, but only globally, even though we know we will all go down the drain?