If they do not comply with the law are they in breach of contract and liable for any damages?
Since this is a statutory right, I doubt it's included in the contract of carriage between you and the airline. On that basis, if it's not a contractual term, they haven't breached the contract itself but they have deprived you of your statutory right.
Assuming you can prove some damage, you could sue them for doing so and they might end up being liable, but I suspect most courts would simply order them to pay the owed refund, your costs, and perhaps a nominal sum for the inconvenience rather than any big pay out.
Normally the airline regulator in your country is responsible for enforcing compliance with this law, so your first port of call would usually be to contact them and complain rather than proceeding straight to court.