"Align" literally means to bring two things into the same order or arrangement. In a figurative sense, it can mean to arrange things in such a way that they work in parallel, or heading in the same direction, towards the same goal.
"Abroad" in this context means "in foreign countries". Most countries have a foreign policy; that is a strategy in dealing with other nations, so the inclusion of the word "abroad" here is to show that the statement applies to what the subject country does in other countries.
"Economic incentives" are policies or programs that boost trade, such as giving tax breaks to a particular industry, at home or abroad, so encourage growth.
"Environmental goals" refers to a country's aims to improve the environment, reduce carbon emissions, etc. In your example, it would seem that these goals are dictated by the "Paris agreement", to which the subject country has committed themselves.
It may be that the incentives already in place to encourage trade with other countries were not good for the environment. So, "aligning our economic incentives abroad with our environmental goals" means adjusting any existing incentives that the country has in place in other countries so that they get results which will help them achieve their targets for improving the environment.